4 apples. 1 definitely good. The remaining 3 each have a 50% chance of being good. So that is an overall probability of 62.5% of picking a good apple from the bag.
Meanwhile for Child A there is only a 50% probability.
If you take it as pure maths and trust that at least 1 of his apples is good, then you've ruled out the permutation where all 3 are bad and left the other 7 permutations where at least one is good.
I think overall that gives you a 12/21 chance of picking a good apple from child A, so about 57%.
Agreeing on the 62.5% on child B, that still, to me, makes B the better bet.
I think you are right on child A but off on child B. Basically, both children have shown the same thing: they have at least one good apple. That rules out the permutation where all apples are bad. That biases the probability of getting a good apple higher, above the basic 50% of the underlying distribution. The size of that bias goes down as the number of apples goes up. With one apple, the bias is worth 50pp: if you know the one apple in the bag is good then your chance of getting a good apple is 100%. With a million apples in the bag, knowing that at least one is good has no effect because the chances of the bag containing no good apples is zero, and so the bias is effectively zero. So you are better off picking from the bag with fewer apples.
Yes, that's my view. Fascinated to hear if I'm wrong because it would be so counter-intuitive.
Chaos in London as thousands of people try a cycle commute for the first time.
I'm likely to have to walk from King's Cross to Waterloo tomorrow. It's not much more than 2 miles, I don't have too much luggage, and it's downhill. Obs buses exist, but I expect they will be rammed
If it’s any help I got an uber today, and it came in minutes and didn’t cost more than normal (to my surprise)
It's an option. But Russell Square is about half way, and there are some nice pubs round there for a break. I'd rather spend money on beer than on taxis
Living in a village, I find that beer and taxis go together.
Foolish to make predictions at this early stage, but if it comes down to Thornberry v Phillipson, it'll be Thornberry. Because Labour's membership is mad.
As @OnlyLivingBoy suggests, the easy way to realise there's a better chance if you choose child A's bag is by upping the number of apples child B has to a million.
Foolish to make predictions at this early stage, but if it comes down to Thornberry v Phillipson, it'll be Thornberry. Because Labour's membership is mad.
All political party members are mad, sane people have better things to do with their time
4 apples. 1 definitely good. The remaining 3 each have a 50% chance of being good. So that is an overall probability of 62.5% of picking a good apple from the bag.
Meanwhile for Child A there is only a 50% probability.
If you take it as pure maths and trust that at least 1 of his apples is good, then you've ruled out the permutation where all 3 are bad and left the other 7 permutations where at least one is good.
I think overall that gives you a 12/21 chance of picking a good apple from child A, so about 57%.
Agreeing on the 62.5% on child B, that still, to me, makes B the better bet.
I think you are right on child A but off on child B. Basically, both children have shown the same thing: they have at least one good apple. That rules out the permutation where all apples are bad. That biases the probability of getting a good apple higher, above the basic 50% of the underlying distribution. The size of that bias goes down as the number of apples goes up. With one apple, the bias is worth 50pp: if you know the one apple in the bag is good then your chance of getting a good apple is 100%. With a million apples in the bag, knowing that at least one is good has no effect because the chances of the bag containing no good apples is zero, and so the bias is effectively zero. So you are better off picking from the bag with fewer apples.
No, I'm sticking to mine. The difference, as I see it, is that child A has confirmed "one of my apples" giving the 7 permutations.
Child B has randomly pulled "one specific apple" that now has 100% chance of being good. Let's suspend that at the point where the apple is out of the bag and consider the probabilities on the 3 remaining apples. Still 50/50 for each of them, no, 8 permutations? Now, put the apple back in - nothing changes, that specific apple remains good, not just "one of my apples".
I think the question comes down to: do you steal an apple from the one with the least apples, or the one who's worked the hardest to collect apples (especially when there are wasps around)
YouGov is consistently giving slightly lower readings for Reform compared to most other pollsters. I'd be interested to know why this might be.
TSE posted about it earlier. They weight down non voters from last time (which is a key Ref support source) Pretty much inverse mirror of FoN approach
Yes, because non-voters are habitual non-voters and habitual non-voters do not vote.
Except when they do which is why even Nigel Farage thought Remain won the Brexit referendum.
As thing stand, the next GE is going to play along very similar lines to the referendum. There is a party with momentum fuelled by a distrust of the status quo, it could be a mistake to discount those who say they’re going to vote for them
Indeed.
There is a reason to question Reform's chances and that is that Nigel Farage has never understood FPTP elections. That is why in previous guises he racked up lots of MEPs and hardly any MPs. Last year, Reform got more votes than the LibDems but Ed Davey has 15 times as many MPs (ironically for a party that claims to believe in proportional representation). Never mind the polls now; on votes last year, Reform is Britain's third party.
But Nigel Farage doesn't get it and doesn't listen to, well, anyone.
It's more complex than that. Farage understands FPTP as well as anyone. The LDs will not be competitive in more than about 100 seats whatever happens. They are in fact content with certainly not winning.
Farage, sadly, has developed bigger ambitions. To win under FPTP you have to present a clear alternative to all others, and be organised in 500-600 seats, and actually try to win in about 450 of them. He has never been in a position to do this before, and he still wouldn't be if Labour had delivered and run stuff brilliantly well.
He can form a government (most seats but not a majority), if he is lucky and we are both unlucky and tactically fail, with about 30% of the vote. Possibly less.
Whereas despite the epic fails of Tory and Labour (so far) the LDs are still in 100 seats absolute max territory.
Genius and luck, momentum optimism and opportunity. Farage will only get one chance. Heaven help the rest of us.
The Apple Puzzle On a tree, half of the apples have holes made by wasps. • One boy picked 3 apples at random and said “at least one of mine has no holes.” • Another boy picked 4 apples similarly. He showed me one of them at random, and it had no holes. He put it back. If you may take just one apple from either boy’s bag, from which boy do you have the better chance of picking an apple without holes?
I don't understand why people are getting into calculations of probability to answer this.
If we assume, as we must, that (i) there are enough apples on the tree for that not to be a factor (ii) the first boy is telling the truth, then: - at least 1/3 of the first boy's apples has no holes; - at least 1/4 of the second boy's apples has no holes. If you can't see that "at least 1/3" is a better chance than "at least 1/4" then that's a bit worrying
Foolish to make predictions at this early stage, but if it comes down to Thornberry v Phillipson, it'll be Thornberry. Because Labour's membership is mad.
All political party members are mad, sane people have better things to do with their time
Also, "which potential leader makes me feel good about myself" tends to beat "which potential leader is most plausible as a national leader"? Which is fair enough for a hobby in a consumerist society, but not optimal as part of a nationwide democracy.
The ratio of good to duff decisions by party memberships is pretty awful.
4 apples. 1 definitely good. The remaining 3 each have a 50% chance of being good. So that is an overall probability of 62.5% of picking a good apple from the bag.
Meanwhile for Child A there is only a 50% probability.
If you take it as pure maths and trust that at least 1 of his apples is good, then you've ruled out the permutation where all 3 are bad and left the other 7 permutations where at least one is good.
I think overall that gives you a 12/21 chance of picking a good apple from child A, so about 57%.
Agreeing on the 62.5% on child B, that still, to me, makes B the better bet.
I think you are right on child A but off on child B. Basically, both children have shown the same thing: they have at least one good apple. That rules out the permutation where all apples are bad. That biases the probability of getting a good apple higher, above the basic 50% of the underlying distribution. The size of that bias goes down as the number of apples goes up. With one apple, the bias is worth 50pp: if you know the one apple in the bag is good then your chance of getting a good apple is 100%. With a million apples in the bag, knowing that at least one is good has no effect because the chances of the bag containing no good apples is zero, and so the bias is effectively zero. So you are better off picking from the bag with fewer apples.
No, I'm sticking to mine. The difference, as I see it, is that child A has confirmed "one of my apples" giving the 7 permutations.
Child B has randomly pulled "one specific apple" that now has 100% chance of being good. Let's suspend that at the point where the apple is out of the bag and consider the probabilities on the 3 remaining apples. Still 50/50 for each of them, no, 8 permutations. Now, put the apple back in - nothing changes, that specific apple remains good, not just "one of my apples".
But there aren’t 6 or 8 permutations - we know 1 apple in each bag is good
So it’s (100%+50%+50%)/3 in bag A and (100%+50%+50%+50%)/4 in bag B
Which is 66% chance of a good apple in bag A and 62.5% in bag B and as you add more apples the percentage will move closer to the 50% odds you would get from selecting a single apple directly from the tree
4 apples. 1 definitely good. The remaining 3 each have a 50% chance of being good. So that is an overall probability of 62.5% of picking a good apple from the bag.
Meanwhile for Child A there is only a 50% probability.
If you take it as pure maths and trust that at least 1 of his apples is good, then you've ruled out the permutation where all 3 are bad and left the other 7 permutations where at least one is good.
I think overall that gives you a 12/21 chance of picking a good apple from child A, so about 57%.
Agreeing on the 62.5% on child B, that still, to me, makes B the better bet.
I think you are right on child A but off on child B. Basically, both children have shown the same thing: they have at least one good apple. That rules out the permutation where all apples are bad. That biases the probability of getting a good apple higher, above the basic 50% of the underlying distribution. The size of that bias goes down as the number of apples goes up. With one apple, the bias is worth 50pp: if you know the one apple in the bag is good then your chance of getting a good apple is 100%. With a million apples in the bag, knowing that at least one is good has no effect because the chances of the bag containing no good apples is zero, and so the bias is effectively zero. So you are better off picking from the bag with fewer apples.
No, I'm sticking to mine. The difference, as I see it, is that child A has confirmed "one of my apples" giving the 7 permutations.
Child B has randomly pulled "one specific apple" that now has 100% chance of being good. Let's suspend that at the point where the apple is out of the bag and consider the probabilities on the 3 remaining apples. Still 50/50 for each of them, no, 8 permutations. Now, put the apple back in - nothing changes, that specific apple remains good, not just "one of my apples".
I don't see what difference it makes that Child B has showed you his good apple, as long as Child A's statement can be assumed to be trustworthy. Once Child B puts his apple back in the bag, you're in the same position as Child A but with one more apple. So the maths become:
Child A: 1 in 3 chance of getting the known good apple, 2 in 3 chance of getting one of the others - which have a 50/50 chance of being good - therefore 1 in 3 plus half of 2 in 3 therefore 1 in 3 plus 1 in 3 therefore a 2 in 3 chance of getting a good apple
Child B: 1 in 4 chance of getting the known good apple, 3 in 4 chance of getting one of the others - which have a 50/50 chance of being good - therefore 1 in 4 plus half of 3 in 4 therefore 1 in 4 plus 1.5 in 4 i.e. 3 in 8 therefore 2 in 8 plus 3 in 8 therefore a 5 in 8 chance of getting a good apple
2 in 3 = 67%, 5 in 8 = 62.5% chance. Therefore Child A gives you a better chance of a good apple.
But please carry on trying to convince me that the reverse is true, because I'd love to be wrong on this - I really like counterintuitive statistics.
Foolish to make predictions at this early stage, but if it comes down to Thornberry v Phillipson, it'll be Thornberry. Because Labour's membership is mad.
All political party members are mad, sane people have better things to do with their time
Also, "which potential leader makes me feel good about myself" tends to beat "which potential leader is most plausible as a national leader"? Which is fair enough for a hobby in a consumerist society, but not optimal as part of a nationwide democracy.
The ratio of good to duff decisions by party memberships is pretty awful.
Have we ever had a party membership election since 2006 where the membership made the sane choice?
The IDF are out of control and seem to think they can do anything they like. And wtf is Starmer doing meeting the Israeli President tomorrow ?
Do you object to them slotting the leaders of Hamas? Those guys are pure evil. Corrupt Islamist murderers, who presumably planned October 7. Good riddance
If only Israel would restrict herself to surgical strikes like this
Since we're not told the percentage of bad apples on the tree
No we're told 50% of the apples are good and 50% are bad.
But we don't know the total number of apples - does that matter?
It’s a tree so I think the fact we are looking at just 7 apples from a tree with say 100 on it makes the 7 picked ones statistically insignificant so the odds on apple quality are still 50%
4 apples. 1 definitely good. The remaining 3 each have a 50% chance of being good. So that is an overall probability of 62.5% of picking a good apple from the bag.
Meanwhile for Child A there is only a 50% probability.
If you take it as pure maths and trust that at least 1 of his apples is good, then you've ruled out the permutation where all 3 are bad and left the other 7 permutations where at least one is good.
I think overall that gives you a 12/21 chance of picking a good apple from child A, so about 57%.
Agreeing on the 62.5% on child B, that still, to me, makes B the better bet.
I think you are right on child A but off on child B. Basically, both children have shown the same thing: they have at least one good apple. That rules out the permutation where all apples are bad. That biases the probability of getting a good apple higher, above the basic 50% of the underlying distribution. The size of that bias goes down as the number of apples goes up. With one apple, the bias is worth 50pp: if you know the one apple in the bag is good then your chance of getting a good apple is 100%. With a million apples in the bag, knowing that at least one is good has no effect because the chances of the bag containing no good apples is zero, and so the bias is effectively zero. So you are better off picking from the bag with fewer apples.
No, I'm sticking to mine. The difference, as I see it, is that child A has confirmed "one of my apples" giving the 7 permutations.
Child B has randomly pulled "one specific apple" that now has 100% chance of being good. Let's suspend that at the point where the apple is out of the bag and consider the probabilities on the 3 remaining apples. Still 50/50 for each of them, no, 8 permutations. Now, put the apple back in - nothing changes, that specific apple remains good, not just "one of my apples".
I don't see what difference it makes that Child B has showed you his good apple, as long as Child A's statement can be assumed to be trustworthy. Once Child B puts his apple back in the bag, you're in the same position as Child A but with one more apple. So the maths become:
Child A: 1 in 3 chance of getting the known good apple, 2 in 3 chance of getting one of the others - which have a 50/50 chance of being good - therefore 1 in 3 plus half of 2 in 3 therefore 1 in 3 plus 1 in 3 therefore a 2 in 3 chance of getting a good apple
Child B: 1 in 4 chance of getting the known good apple, 3 in 4 chance of getting one of the others - which have a 50/50 chance of being good - therefore 1 in 4 plus half of 3 in 4 therefore 1 in 4 plus 1.5 in 4 i.e. 3 in 8 therefore 2 in 8 plus 3 in 8 therefore a 5 in 8 chance of getting a good apple
2 in 3 = 67%, 5 in 8 = 62.5% chance. Therefore Child A gives you a better chance of a good apple.
But please carry on trying to convince me that the reverse is true, because I'd love to be wrong on this - I really like counterintuitive statistics.
This is what I did, but then I was left wondering about the tree and how many apples to begin with. The maths above assumes A and B are picking from two identical trees rather than B picking after A has picked and not replaced.
Foolish to make predictions at this early stage, but if it comes down to Thornberry v Phillipson, it'll be Thornberry. Because Labour's membership is mad.
All political party members are mad, sane people have better things to do with their time
Also, "which potential leader makes me feel good about myself" tends to beat "which potential leader is most plausible as a national leader"? Which is fair enough for a hobby in a consumerist society, but not optimal as part of a nationwide democracy.
The ratio of good to duff decisions by party memberships is pretty awful.
Have we ever had a party membership election since 2006 where the membership made the sane choice?
2020 Liberal Democrats leadership election: Davey beat Moran.
The mandelson birthday message to Epstein is also *awkward*
What is the “wonderful secret” he shared with his “best pal” Epstein who he also “loved”?
I rather dismissed this earlier today. But on examination I think Mandelson could be in trouble
Isn't there a problematic diplomatic angle here for Britain?
If Mandelson is forced to resign because of documentary evidence that he did something that Trump has also done exactly, then Britain is implicitly making a judgement on Trump's fitness for office.
4 apples. 1 definitely good. The remaining 3 each have a 50% chance of being good. So that is an overall probability of 62.5% of picking a good apple from the bag.
Meanwhile for Child A there is only a 50% probability.
If you take it as pure maths and trust that at least 1 of his apples is good, then you've ruled out the permutation where all 3 are bad and left the other 7 permutations where at least one is good.
I think overall that gives you a 12/21 chance of picking a good apple from child A, so about 57%.
Agreeing on the 62.5% on child B, that still, to me, makes B the better bet.
I think you are right on child A but off on child B. Basically, both children have shown the same thing: they have at least one good apple. That rules out the permutation where all apples are bad. That biases the probability of getting a good apple higher, above the basic 50% of the underlying distribution. The size of that bias goes down as the number of apples goes up. With one apple, the bias is worth 50pp: if you know the one apple in the bag is good then your chance of getting a good apple is 100%. With a million apples in the bag, knowing that at least one is good has no effect because the chances of the bag containing no good apples is zero, and so the bias is effectively zero. So you are better off picking from the bag with fewer apples.
No, I'm sticking to mine. The difference, as I see it, is that child A has confirmed "one of my apples" giving the 7 permutations.
Child B has randomly pulled "one specific apple" that now has 100% chance of being good. Let's suspend that at the point where the apple is out of the bag and consider the probabilities on the 3 remaining apples. Still 50/50 for each of them, no, 8 permutations? Now, put the apple back in - nothing changes, that specific apple remains good, not just "one of my apples".
Yes, I think you're right, and have changed my mind.
By taking one out and putting it back, child B has changed the sample from a random one of four apples to a randomly picked group of three - identical in respect of selection - to child A's, PLUS a good apple.
While child A has told us something about his whole set of three, child B has changed his set to three random choices, plus a known quantity.
The IDF are out of control and seem to think they can do anything they like. And wtf is Starmer doing meeting the Israeli President tomorrow ?
Hopefully that’s been removed from the calendar as we speak because of today’s attack on foreign soil
Israel has been regularly attacking foreign soil for months. They were bombing Syria a few days ago, for example. It's not like this new attack is out of the ordinary.
Chaos in London as thousands of people try a cycle commute for the first time.
I'm likely to have to walk from King's Cross to Waterloo tomorrow. It's not much more than 2 miles, I don't have too much luggage, and it's downhill. Obs buses exist, but I expect they will be rammed
If it’s any help I got an uber today, and it came in minutes and didn’t cost more than normal (to my surprise)
It's an option. But Russell Square is about half way, and there are some nice pubs round there for a break. I'd rather spend money on beer than on taxis
Don't be fooled. Russell Square is about one third, perhaps slightly less, of the walk from King's Cross to Waterloo. The half way mark is more like Holborn tube.
The mandelson birthday message to Epstein is also *awkward*
What is the “wonderful secret” he shared with his “best pal” Epstein who he also “loved”?
I rather dismissed this earlier today. But on examination I think Mandelson could be in trouble
Isn't there a problematic diplomatic angle here for Britain?
If Mandelson is forced to resign because of documentary evidence that he did something that Trump has also done exactly, then Britain is implicitly making a judgement on Trump's fitness for office.
And vice versa.
I’m not sure it’s that complex or subtle
Mandelson will have to speak on this. The birthday message is kind of nauseating (like Trump’s). What does he mean by “yum yum”. Is Mandelson referring to the excellent breakfasts Epstein laid on at Lolita island?
The mandelson birthday message to Epstein is also *awkward*
What is the “wonderful secret” he shared with his “best pal” Epstein who he also “loved”?
I rather dismissed this earlier today. But on examination I think Mandelson could be in trouble
Isn't there a problematic diplomatic angle here for Britain?
If Mandelson is forced to resign because of documentary evidence that he did something that Trump has also done exactly, then Britain is implicitly making a judgement on Trump's fitness for office.
And vice versa.
Yes
Sacking Mandelson would send an explicit message.
Which is why it won't happen, and also why it should.
The Apple Puzzle On a tree, half of the apples have holes made by wasps. • One boy picked 3 apples at random and said “at least one of mine has no holes.” • Another boy picked 4 apples similarly. He showed me one of them at random, and it had no holes. He put it back. If you may take just one apple from either boy’s bag, from which boy do you have the better chance of picking an apple without holes?
I don't understand why people are getting into calculations of probability to answer this.
If we assume, as we must, that (i) there are enough apples on the tree for that not to be a factor (ii) the first boy is telling the truth, then: - at least 1/3 of the first boy's apples has no holes; - at least 1/4 of the second boy's apples has no holes. If you can't see that "at least 1/3" is a better chance than "at least 1/4" then that's a bit worrying
I think this is a more complex example of the Monty Hall problem, though. Both sets are altered from random ones by the act of observation.
Foolish to make predictions at this early stage, but if it comes down to Thornberry v Phillipson, it'll be Thornberry. Because Labour's membership is mad.
All political party members are mad, sane people have better things to do with their time
Also, "which potential leader makes me feel good about myself" tends to beat "which potential leader is most plausible as a national leader"? Which is fair enough for a hobby in a consumerist society, but not optimal as part of a nationwide democracy.
The ratio of good to duff decisions by party memberships is pretty awful.
Have we ever had a party membership election since 2006 where the membership made the sane choice?
I'd say Labour made the sanest available choice in 2020- however mediocre Starmer is, Long-Bailey would have been a disaster and Nandy is even less up to it than Boring Old Keir.
In both cases, it implies that the membership can be forced to leave their comfort zone, but only after multiple defeats.
US green lit the Qatar attack. Middle East is about to erupt (more)
Or - being absurdly hopeful, but let’s try - it might hasten the end of this satanic war. Hamas need to be exterminated. Peace is impossible as long as they have any power in Gaza. Killing all the leaders is not very nice but who knows - it could work for the Gazans (only 4% of whom actually want Hamas to be their government)
I wonder how many Gazans are secretly pleased today
I have no time for Mandelson but it’s obvious he wouldn’t be interested in under age girls . So it’s a nothing burger . More questions should be aimed at Trump and his creepy birthday message .
Er, Epstein has also been accused of molesting boys
Again - I don’t think we can so easily exonerate anyone who was close to Epstein. That goes for left or right - Clinton or Trump. Or royal or famous or billionaire or whatever
Qatar says it "strongly condemns the cowardly Israeli attack that targeted residential buildings housing several members of the Political Bureau of Hamas ... This criminal assault constitutes a blatant violation of all international laws and norms."
I have no time for Mandelson but it’s obvious he wouldn’t be interested in under age girls . So it’s a nothing burger . More questions should be aimed at Trump and his creepy birthday message .
Er, Epstein has also been accused of molesting boys
Again - I don’t think we can so easily exonerate anyone who was close to Epstein. That goes for left or right - Clinton or Trump. Or royal or famous or billionaire or whatever
If the tree has 8 apples in total (A 7 apple tree will not give an initial underlying 50-50 probability), rather than a large number then can extend child A's apples left: Eliminated: 1 spaces of HHH - left (HNNNN)
The space eliminated is the best possible space for the second child so actually it makes no difference that the first child's bag is better whether we have a large number of apples or a small number assuming replacement or no replacement and even if the underlying probability isn't 50% we're still better off choosing child A (See @Occasionalranter work)
4 apples. 1 definitely good. The remaining 3 each have a 50% chance of being good. So that is an overall probability of 62.5% of picking a good apple from the bag.
Meanwhile for Child A there is only a 50% probability.
If you take it as pure maths and trust that at least 1 of his apples is good, then you've ruled out the permutation where all 3 are bad and left the other 7 permutations where at least one is good.
I think overall that gives you a 12/21 chance of picking a good apple from child A, so about 57%.
Agreeing on the 62.5% on child B, that still, to me, makes B the better bet.
I think you are right on child A but off on child B. Basically, both children have shown the same thing: they have at least one good apple. That rules out the permutation where all apples are bad. That biases the probability of getting a good apple higher, above the basic 50% of the underlying distribution. The size of that bias goes down as the number of apples goes up. With one apple, the bias is worth 50pp: if you know the one apple in the bag is good then your chance of getting a good apple is 100%. With a million apples in the bag, knowing that at least one is good has no effect because the chances of the bag containing no good apples is zero, and so the bias is effectively zero. So you are better off picking from the bag with fewer apples.
No, I'm sticking to mine. The difference, as I see it, is that child A has confirmed "one of my apples" giving the 7 permutations.
Child B has randomly pulled "one specific apple" that now has 100% chance of being good. Let's suspend that at the point where the apple is out of the bag and consider the probabilities on the 3 remaining apples. Still 50/50 for each of them, no, 8 permutations. Now, put the apple back in - nothing changes, that specific apple remains good, not just "one of my apples".
I don't see what difference it makes that Child B has showed you his good apple, as long as Child A's statement can be assumed to be trustworthy. Once Child B puts his apple back in the bag, you're in the same position as Child A but with one more apple. So the maths become:
Child A: 1 in 3 chance of getting the known good apple, 2 in 3 chance of getting one of the others - which have a 50/50 chance of being good - therefore 1 in 3 plus half of 2 in 3 therefore 1 in 3 plus 1 in 3 therefore a 2 in 3 chance of getting a good apple
Child B: 1 in 4 chance of getting the known good apple, 3 in 4 chance of getting one of the others - which have a 50/50 chance of being good - therefore 1 in 4 plus half of 3 in 4 therefore 1 in 4 plus 1.5 in 4 i.e. 3 in 8 therefore 2 in 8 plus 3 in 8 therefore a 5 in 8 chance of getting a good apple
2 in 3 = 67%, 5 in 8 = 62.5% chance. Therefore Child A gives you a better chance of a good apple.
But please carry on trying to convince me that the reverse is true, because I'd love to be wrong on this - I really like counterintuitive statistics.
Thing is, B has picked an apple from his bag of 4 *at random* and it was good. A has looked at all 3 and on that basis has made his "at least one is good" statement. There is a difference there, I think, and ProRata's calc adjusts for this.
I haven't read the intermediate 300 posts (sorry), but the "we know Boris Johnson is a self-serving, shitty liar so leave him alone because his dodgy receipt of hundreds of thousands about which he lied" is therefore a nothingburger, alongside "Rayner delenda est" for £40k because she did not know complex law, seems ... strange.
Do we even know that Johnson had not misused his "for public duties" £115k a year? It would be entirely in character for him to misuse it for personal profit.
I'd be looking for a decent enquiry by a Judge, and then a tighter system which is effectively enforced. Boris will squeal Just William style, but sod that - hold the swine to account.
Boris had one enquiry before, which found him to be But because it was a Parliamentary Enquiry he could dodge it by running away:
... when he received the draft of the Commons Privileges Committee investigation into his conduct that unanimously found that he had lied to the Commons on numerous occasions. Johnson resigned his position as MP the same day. https://en.wikipedia.org/wiki/Boris_Johnson
US green lit the Qatar attack. Middle East is about to erupt (more)
Or - being absurdly hopeful, but let’s try - it might hasten the end of this satanic war. Hamas need to be exterminated. Peace is impossible as long as they have any power in Gaza. Killing all the leaders is not very nice but who knows - it could work for the Gazans (only 4% of whom actually want Hamas to be their government)
I wonder how many Gazans are secretly pleased today
I see that, yes, but there is also the need to manage the relationship with the rest of the ME for the longer term. High risk stuff.
US green lit the Qatar attack. Middle East is about to erupt (more)
Or - being absurdly hopeful, but let’s try - it might hasten the end of this satanic war. Hamas need to be exterminated. Peace is impossible as long as they have any power in Gaza. Killing all the leaders is not very nice but who knows - it could work for the Gazans (only 4% of whom actually want Hamas to be their government)
I wonder how many Gazans are secretly pleased today
I see that, yes, but there is also the need to manage the relationship with the rest of the ME for the longer term. High risk stuff.
I’m getting on a plane to the sun so I’m in a benign and optimistic mood
This should go down well in Doha. "US President Donald Trump gave the green light for the Israeli strike in Qatar, a senior Israeli official tells Channel 12."
The mandelson birthday message to Epstein is also *awkward*
What is the “wonderful secret” he shared with his “best pal” Epstein who he also “loved”?
I rather dismissed this earlier today. But on examination I think Mandelson could be in trouble
Isn't there a problematic diplomatic angle here for Britain?
If Mandelson is forced to resign because of documentary evidence that he did something that Trump has also done exactly, then Britain is implicitly making a judgement on Trump's fitness for office.
And vice versa.
Interesting point. It would put Mandelson as the top news story in the US, relentless leveraged by the media for weeks.
Reports in Israel targeted Hamas leadership was meeting to examine Trump's ceasefire proposal. Who would negotiate with the US after this, and the attack on Iran? Death blow to any remaining US credibility in MENA and beyond.
I have seen it suggested Donny should admit to the Epstein letter and try and win the Literature prize instead...
I’m in a lounge at LHR T3 and I’m getting “concierge service”
A gentleman named Elvis is going to escort me from the lounge to my gate, to carry my luggage and ensure I make the flight
He really is called Elvis
Is this included in flying first class?
No I’m in Economy (it’s only to Sardinia)
But I’m travelling with a mega posh travel company, writing about them. This is one of the things they do for their customers. It’s like having a butler all the way through the trip - I’ve experienced it before. They are on call 24/7 to do anything you need. Sort your laundry. Book a restaurant. Choose a hike. Probably sexual favours
I can report that Elvis and his friend escorted me all of the 200 yards from the lounge to the gate
US green lit the Qatar attack. Middle East is about to erupt (more)
Or - being absurdly hopeful, but let’s try - it might hasten the end of this satanic war. Hamas need to be exterminated. Peace is impossible as long as they have any power in Gaza. Killing all the leaders is not very nice but who knows - it could work for the Gazans (only 4% of whom actually want Hamas to be their government)
I wonder how many Gazans are secretly pleased today
Your abject lack of insight into the lives other people lead continues to amaze. Really you should try and travel more, to broaden your horizons.
Meanwhile, minimal notice of this act of terrorism.
At least 21 civilians were killed and more than two dozen injured following a barbaric direct Russian strike with an air bomb on ordinary people lined up to receive pensions in the village of Yarova in the Donetsk region.. https://x.com/andrii_sybiha/status/1965355437663916266
The Apple Puzzle On a tree, half of the apples have holes made by wasps. • One boy picked 3 apples at random and said “at least one of mine has no holes.” • Another boy picked 4 apples similarly. He showed me one of them at random, and it had no holes. He put it back. If you may take just one apple from either boy’s bag, from which boy do you have the better chance of picking an apple without holes?
I don't understand why people are getting into calculations of probability to answer this.
If we assume, as we must, that (i) there are enough apples on the tree for that not to be a factor (ii) the first boy is telling the truth, then: - at least 1/3 of the first boy's apples has no holes; - at least 1/4 of the second boy's apples has no holes. If you can't see that "at least 1/3" is a better chance than "at least 1/4" then that's a bit worrying
I think this is a more complex example of the Monty Hall problem, though. Both sets are altered from random ones by the act of observation.
I don't think it is. In the Monty Hall problem, if we call door 1 the door you picked, then seeing what's behind one other particular door tells you that there is a greater chance than you first assumed that the unpicked unopened door has a car behind it. Here, even though in boy B's case you do get to see a particular apple, you don't get to track that apple so it's not more useful information than merely being told that at least one apple is good.
IMPORTANT: A senior Hamas source told Al Jazeera that the movement’s leadership delegation, headed by Khalil al-Hayya, survived an Israeli assassination attempt carried out through an airstrike in Doha.
The Apple Puzzle On a tree, half of the apples have holes made by wasps. • One boy picked 3 apples at random and said “at least one of mine has no holes.” • Another boy picked 4 apples similarly. He showed me one of them at random, and it had no holes. He put it back. If you may take just one apple from either boy’s bag, from which boy do you have the better chance of picking an apple without holes?
I don't understand why people are getting into calculations of probability to answer this.
If we assume, as we must, that (i) there are enough apples on the tree for that not to be a factor (ii) the first boy is telling the truth, then: - at least 1/3 of the first boy's apples has no holes; - at least 1/4 of the second boy's apples has no holes. If you can't see that "at least 1/3" is a better chance than "at least 1/4" then that's a bit worrying
I think this is a more complex example of the Monty Hall problem, though. Both sets are altered from random ones by the act of observation.
I don't think it is. In the Monty Hall problem, if we call door 1 the door you picked, then seeing what's behind one other particular door tells you that there is a greater chance than you first assumed that the unpicked unopened door has a car behind it. Here, even though in boy B's case you do get to see a particular apple, you don't get to track that apple so it's not more useful information than merely being told that at least one apple is good.
But: great reference. I love the Monty Hall problem. I managed to argue about it for a solid hour and a half with an actuary colleague a long time ago, in a pub, and it was very thirsty work. Of course, I was wrong and had to concede eventually, so let's see how this goes
IMPORTANT: A senior Hamas source told Al Jazeera that the movement’s leadership delegation, headed by Khalil al-Hayya, survived an Israeli assassination attempt carried out through an airstrike in Doha.
I thought Qatar had kicked them all out and they had gone to Turkey where they own billions in real estate?
If they really want to upset Banksy, cut out the piece of wall, and auction it to some billionaires.
Everybody knows who he / they are anyway. They have been caught on camera a number of times and I am sure if people can be bothered a bit of a game of follow the money will prove it.
The mandelson birthday message to Epstein is also *awkward*
What is the “wonderful secret” he shared with his “best pal” Epstein who he also “loved”?
I rather dismissed this earlier today. But on examination I think Mandelson could be in trouble
The "wonderful secret" is in the Trump letter.
This is Mandelson. “Once upon a time, an intelligent, sharp-witted man they call ‘mysterious’ parachuted into my life … you would spend many hours just waiting for him to turn up … And often, no sooner were you used to having him around, you would suddenly be alone again … Leaving you with some ‘interesting’ friends to entertain instead … Or just some dogs* to keep you company (he wasn’t always so keen on them) … But then he would parachute back in … Very occasionally, taking you by surprise in some far off places … Or in one of his glorious homes he likes to share with his friends (yum yum) … But wherever he is in the world, he remains my best pal!”
*Mandelson had, I think, two labradors at the time.
Prosecution is too good for Mandelson.
That kind of writing deserves something far more... fatal.
4 apples. 1 definitely good. The remaining 3 each have a 50% chance of being good. So that is an overall probability of 62.5% of picking a good apple from the bag.
Meanwhile for Child A there is only a 50% probability.
If you take it as pure maths and trust that at least 1 of his apples is good, then you've ruled out the permutation where all 3 are bad and left the other 7 permutations where at least one is good.
I think overall that gives you a 12/21 chance of picking a good apple from child A, so about 57%.
Agreeing on the 62.5% on child B, that still, to me, makes B the better bet.
I think you are right on child A but off on child B. Basically, both children have shown the same thing: they have at least one good apple. That rules out the permutation where all apples are bad. That biases the probability of getting a good apple higher, above the basic 50% of the underlying distribution. The size of that bias goes down as the number of apples goes up. With one apple, the bias is worth 50pp: if you know the one apple in the bag is good then your chance of getting a good apple is 100%. With a million apples in the bag, knowing that at least one is good has no effect because the chances of the bag containing no good apples is zero, and so the bias is effectively zero. So you are better off picking from the bag with fewer apples.
No, I'm sticking to mine. The difference, as I see it, is that child A has confirmed "one of my apples" giving the 7 permutations.
Child B has randomly pulled "one specific apple" that now has 100% chance of being good. Let's suspend that at the point where the apple is out of the bag and consider the probabilities on the 3 remaining apples. Still 50/50 for each of them, no, 8 permutations. Now, put the apple back in - nothing changes, that specific apple remains good, not just "one of my apples".
I don't see what difference it makes that Child B has showed you his good apple, as long as Child A's statement can be assumed to be trustworthy. Once Child B puts his apple back in the bag, you're in the same position as Child A but with one more apple. So the maths become:
Child A: 1 in 3 chance of getting the known good apple, 2 in 3 chance of getting one of the others - which have a 50/50 chance of being good - therefore 1 in 3 plus half of 2 in 3 therefore 1 in 3 plus 1 in 3 therefore a 2 in 3 chance of getting a good apple
Child B: 1 in 4 chance of getting the known good apple, 3 in 4 chance of getting one of the others - which have a 50/50 chance of being good - therefore 1 in 4 plus half of 3 in 4 therefore 1 in 4 plus 1.5 in 4 i.e. 3 in 8 therefore 2 in 8 plus 3 in 8 therefore a 5 in 8 chance of getting a good apple
2 in 3 = 67%, 5 in 8 = 62.5% chance. Therefore Child A gives you a better chance of a good apple.
But please carry on trying to convince me that the reverse is true, because I'd love to be wrong on this - I really like counterintuitive statistics.
Thing is, B has picked an apple from his bag of 4 *at random* and it was good. A has looked at all 3 and on that basis has made his "at least one is good" statement. There is a difference there, I think, and ProRata's calc adjusts for this.
What evidence do we have the apple was pulled out at random? I read it as child B showing an apple to demonstrate that at least one apple is good, having seen the full distribution of apples in the bag.
The Apple Puzzle On a tree, half of the apples have holes made by wasps. • One boy picked 3 apples at random and said “at least one of mine has no holes.” • Another boy picked 4 apples similarly. He showed me one of them at random, and it had no holes. He put it back. If you may take just one apple from either boy’s bag, from which boy do you have the better chance of picking an apple without holes?
I don't understand why people are getting into calculations of probability to answer this.
If we assume, as we must, that (i) there are enough apples on the tree for that not to be a factor (ii) the first boy is telling the truth, then: - at least 1/3 of the first boy's apples has no holes; - at least 1/4 of the second boy's apples has no holes. If you can't see that "at least 1/3" is a better chance than "at least 1/4" then that's a bit worrying
I think this is a more complex example of the Monty Hall problem, though. Both sets are altered from random ones by the act of observation.
I don't think it is. In the Monty Hall problem, if we call door 1 the door you picked, then seeing what's behind one other particular door tells you that there is a greater chance than you first assumed that the unpicked unopened door has a car behind it. Here, even though in boy B's case you do get to see a particular apple, you don't get to track that apple so it's not more useful information than merely being told that at least one apple is good.
No, that's incorrect. Each of the four apples has a 50/50 chance of being good or bad, prior to one of them being checked at random. After that, three of them still have that 50/50 chance, as they haven't been observed, and the fourth is 100% likely to be good, and is available to be picked again.
That gives you a 62.5% of picking a good apple from the four.
4 apples. 1 definitely good. The remaining 3 each have a 50% chance of being good. So that is an overall probability of 62.5% of picking a good apple from the bag.
Meanwhile for Child A there is only a 50% probability.
If you take it as pure maths and trust that at least 1 of his apples is good, then you've ruled out the permutation where all 3 are bad and left the other 7 permutations where at least one is good.
I think overall that gives you a 12/21 chance of picking a good apple from child A, so about 57%.
Agreeing on the 62.5% on child B, that still, to me, makes B the better bet.
I think you are right on child A but off on child B. Basically, both children have shown the same thing: they have at least one good apple. That rules out the permutation where all apples are bad. That biases the probability of getting a good apple higher, above the basic 50% of the underlying distribution. The size of that bias goes down as the number of apples goes up. With one apple, the bias is worth 50pp: if you know the one apple in the bag is good then your chance of getting a good apple is 100%. With a million apples in the bag, knowing that at least one is good has no effect because the chances of the bag containing no good apples is zero, and so the bias is effectively zero. So you are better off picking from the bag with fewer apples.
No, I'm sticking to mine. The difference, as I see it, is that child A has confirmed "one of my apples" giving the 7 permutations.
Child B has randomly pulled "one specific apple" that now has 100% chance of being good. Let's suspend that at the point where the apple is out of the bag and consider the probabilities on the 3 remaining apples. Still 50/50 for each of them, no, 8 permutations. Now, put the apple back in - nothing changes, that specific apple remains good, not just "one of my apples".
I don't see what difference it makes that Child B has showed you his good apple, as long as Child A's statement can be assumed to be trustworthy. Once Child B puts his apple back in the bag, you're in the same position as Child A but with one more apple. So the maths become:
Child A: 1 in 3 chance of getting the known good apple, 2 in 3 chance of getting one of the others - which have a 50/50 chance of being good - therefore 1 in 3 plus half of 2 in 3 therefore 1 in 3 plus 1 in 3 therefore a 2 in 3 chance of getting a good apple
Child B: 1 in 4 chance of getting the known good apple, 3 in 4 chance of getting one of the others - which have a 50/50 chance of being good - therefore 1 in 4 plus half of 3 in 4 therefore 1 in 4 plus 1.5 in 4 i.e. 3 in 8 therefore 2 in 8 plus 3 in 8 therefore a 5 in 8 chance of getting a good apple
2 in 3 = 67%, 5 in 8 = 62.5% chance. Therefore Child A gives you a better chance of a good apple.
But please carry on trying to convince me that the reverse is true, because I'd love to be wrong on this - I really like counterintuitive statistics.
Thing is, B has picked an apple from his bag of 4 *at random* and it was good. A has looked at all 3 and on that basis has made his "at least one is good" statement. There is a difference there, I think, and ProRata's calc adjusts for this.
What evidence do we have the apple was pulled out at random? I read it as child B showing an apple to demonstrate that at least one apple is good, having seen the full distribution of apples in the bag.
The problem was stated by the setter in two different posts, differently.
The Apple Puzzle On a tree, half of the apples have holes made by wasps. • One boy picked 3 apples at random and said “at least one of mine has no holes.” • Another boy picked 4 apples similarly. He showed me one of them at random, and it had no holes. He put it back. If you may take just one apple from either boy’s bag, from which boy do you have the better chance of picking an apple without holes?
I don't understand why people are getting into calculations of probability to answer this.
If we assume, as we must, that (i) there are enough apples on the tree for that not to be a factor (ii) the first boy is telling the truth, then: - at least 1/3 of the first boy's apples has no holes; - at least 1/4 of the second boy's apples has no holes. If you can't see that "at least 1/3" is a better chance than "at least 1/4" then that's a bit worrying
I think this is a more complex example of the Monty Hall problem, though. Both sets are altered from random ones by the act of observation.
I don't think it is. In the Monty Hall problem, if we call door 1 the door you picked, then seeing what's behind one other particular door tells you that there is a greater chance than you first assumed that the unpicked unopened door has a car behind it. Here, even though in boy B's case you do get to see a particular apple, you don't get to track that apple so it's not more useful information than merely being told that at least one apple is good.
I think it is because he picked one at random from his 4. That is a more powerful "at least one is good" attribute compared to looking at all 4 and then making the (true) statement.
The remaining 3 remain a random selection unaffected by the removal - assuming it was a tree with many many apples rather than just a small number. Since in the latter case picking one at random that's good means the remainder is biased towards bad - like if you pick a red playing card from a randomly shuffled pack you leave a bias towards black in the remainder.
So I think ProRata has the best answer - you should pick B.
4 apples. 1 definitely good. The remaining 3 each have a 50% chance of being good. So that is an overall probability of 62.5% of picking a good apple from the bag.
Meanwhile for Child A there is only a 50% probability.
If you take it as pure maths and trust that at least 1 of his apples is good, then you've ruled out the permutation where all 3 are bad and left the other 7 permutations where at least one is good.
I think overall that gives you a 12/21 chance of picking a good apple from child A, so about 57%.
Agreeing on the 62.5% on child B, that still, to me, makes B the better bet.
I think you are right on child A but off on child B. Basically, both children have shown the same thing: they have at least one good apple. That rules out the permutation where all apples are bad. That biases the probability of getting a good apple higher, above the basic 50% of the underlying distribution. The size of that bias goes down as the number of apples goes up. With one apple, the bias is worth 50pp: if you know the one apple in the bag is good then your chance of getting a good apple is 100%. With a million apples in the bag, knowing that at least one is good has no effect because the chances of the bag containing no good apples is zero, and so the bias is effectively zero. So you are better off picking from the bag with fewer apples.
No, I'm sticking to mine. The difference, as I see it, is that child A has confirmed "one of my apples" giving the 7 permutations.
Child B has randomly pulled "one specific apple" that now has 100% chance of being good. Let's suspend that at the point where the apple is out of the bag and consider the probabilities on the 3 remaining apples. Still 50/50 for each of them, no, 8 permutations. Now, put the apple back in - nothing changes, that specific apple remains good, not just "one of my apples".
I don't see what difference it makes that Child B has showed you his good apple, as long as Child A's statement can be assumed to be trustworthy. Once Child B puts his apple back in the bag, you're in the same position as Child A but with one more apple. So the maths become:
Child A: 1 in 3 chance of getting the known good apple, 2 in 3 chance of getting one of the others - which have a 50/50 chance of being good - therefore 1 in 3 plus half of 2 in 3 therefore 1 in 3 plus 1 in 3 therefore a 2 in 3 chance of getting a good apple
Child B: 1 in 4 chance of getting the known good apple, 3 in 4 chance of getting one of the others - which have a 50/50 chance of being good - therefore 1 in 4 plus half of 3 in 4 therefore 1 in 4 plus 1.5 in 4 i.e. 3 in 8 therefore 2 in 8 plus 3 in 8 therefore a 5 in 8 chance of getting a good apple
2 in 3 = 67%, 5 in 8 = 62.5% chance. Therefore Child A gives you a better chance of a good apple.
But please carry on trying to convince me that the reverse is true, because I'd love to be wrong on this - I really like counterintuitive statistics.
Thing is, B has picked an apple from his bag of 4 *at random* and it was good. A has looked at all 3 and on that basis has made his "at least one is good" statement. There is a difference there, I think, and ProRata's calc adjusts for this.
What evidence do we have the apple was pulled out at random? I read it as child B showing an apple to demonstrate that at least one apple is good, having seen the full distribution of apples in the bag.
The Apple Puzzle On a tree, half of the apples have holes made by wasps. • One boy picked 3 apples at random and said “at least one of mine has no holes.” • Another boy picked 4 apples similarly. He showed me one of them at random, and it had no holes. He put it back. If you may take just one apple from either boy’s bag, from which boy do you have the better chance of picking an apple without holes?
If they really want to upset Banksy, cut out the piece of wall, and auction it to some billionaires.
Everybody knows who he / they are anyway. They have been caught on camera a number of times and I am sure if people can be bothered a bit of a game of follow the money will prove it.
If they really want to upset Banksy, cut out the piece of wall, and auction it to some billionaires.
I think a jury would be reluctant to convict. That would play out either as it not being proved that the mural was "damage" or as accepting an "honestly held belief" that HMCTS or whoever is in charge of the building would have consented to the "damage".
We have been warned: Zia Yusuf @ZiaYusufUK · 7h Reform will transform the civil service from a bloated, failed organisation hostile to the interests of the British people into a lean, performant machine that makes our country proud. 🇬🇧
On the face of it, this doesn't sound like anything to be worried about. What do you see as problematic with it?
This is obvious by now, surely? It's about 97% likely to be pure BS. Reform are an incompetent policy-free slogan machine, hoping that fools will fall for it. I doubt if they even know what they mean themselves by "Civil Service", never mind what it actually means.
We have this exact cycle from Zia himself in Kent County Council. Lots of "we will save X Y and Z". But LTNs to be cut did not exist. Woke waste to be cut did not exist. "DEI jobs" hardly existed.
It was all public information, but the numpties of Reform, including Zia himself, did not do any homework. So then he rifled through last year's local papers and social media, to find some identified savings he could claim to have "identified". And made a serious of fake claims about it. Cue a public faceplant.
So what happens next? Well, in Derbyshire they cut half the adult education centres. They had time for a proper process, but waited until the last minute and tried to do an emergency decision.
But RefUK are such a fuckwit collective that they had to admit their action was unlawful.
Vote for a clown show, and you get a circus. I don't want a circus in my Council or Government.
Haha - you think the last or the current government are competent?
The last one - incompetent. The current one - too early to tell.
You thing a Farage Farrago would be less incompetent?
How did that work out in County Councils?
Far too early to tell.
Hmmmm.
Four months since the May elections.
Reform officials failure to obey the law and follow the rules, even on a basic level, says imo that we have plenty of evidence, without even getting into their attacks on scrutiny.
Just to take one, when the Chief Executive of Warwickshire refused to obey an attempted instruction by the leader of the minority Reform UK group, the minority Council Leader, to take down a flag and informed him of the correct procedure which required consent of the whole Council, his next step was to accuse her of being deliberate Civil Service obstructionism against his aims.
It was BS, but Farage still used it as an example in his conference speech.
Like Trump, they are trying to destroy checks, balances and scrutiny.
I think the poisonous nature of RefUK is out there in letters a mile high.
I'd prefer not to repeatedly call Reform UK politicians liars, but it is what they are.
IMPORTANT: A senior Hamas source told Al Jazeera that the movement’s leadership delegation, headed by Khalil al-Hayya, survived an Israeli assassination attempt carried out through an airstrike in Doha.
I thought Qatar had kicked them all out and they had gone to Turkey where they own billions in real estate?
The number of workers on payrolls will likely be revised down by 911,000 for the 12 months through March — or nearly 76,000 less each month — according to the government’s preliminary benchmark revision.
We have been warned: Zia Yusuf @ZiaYusufUK · 7h Reform will transform the civil service from a bloated, failed organisation hostile to the interests of the British people into a lean, performant machine that makes our country proud. 🇬🇧
On the face of it, this doesn't sound like anything to be worried about. What do you see as problematic with it?
This is obvious by now, surely? It's about 97% likely to be pure BS. Reform are an incompetent policy-free slogan machine, hoping that fools will fall for it. I doubt if they even know what they mean themselves by "Civil Service", never mind what it actually means.
We have this exact cycle from Zia himself in Kent County Council. Lots of "we will save X Y and Z". But LTNs to be cut did not exist. Woke waste to be cut did not exist. "DEI jobs" hardly existed.
It was all public information, but the numpties of Reform, including Zia himself, did not do any homework. So then he rifled through last year's local papers and social media, to find some identified savings he could claim to have "identified". And made a serious of fake claims about it. Cue a public faceplant.
So what happens next? Well, in Derbyshire they cut half the adult education centres. They had time for a proper process, but waited until the last minute and tried to do an emergency decision.
But RefUK are such a fuckwit collective that they had to admit their action was unlawful.
Vote for a clown show, and you get a circus. I don't want a circus in my Council or Government.
Haha - you think the last or the current government are competent?
The last one - incompetent. The current one - too early to tell.
You thing a Farage Farrago would be less incompetent?
How did that work out in County Councils?
Far too early to tell.
Hmmmm.
Four months since the May elections.
Reform officials failure to obey the law and follow the rules, even on a basic level, says imo that we have plenty of evidence, without even getting into their attacks on scrutiny.
Just to take one, when the Chief Executive of Warwickshire refused to obey an attempted instruction by the leader of the minority Reform UK group, the minority Council Leader, to take down a flag and informed him of the correct procedure which required consent of the whole Council, his next step was to accuse her of being deliberate Civil Service obstructionism against his aims.
It was BS, but Farage still used it as an example in his conference speech.
Like Trump, they are trying to destroy checks, balances and scrutiny.
I think the poisonous nature of RefUK is out there in letters a mile high.
I'd prefer not to repeatedly call Reform UK politicians liars, but it is what they are.
If Labour and co want to win the next election they need to call Reform out every time they lie until it finally dawns on Reform supporters that they are being tricked by liars
The Apple Puzzle On a tree, half of the apples have holes made by wasps. • One boy picked 3 apples at random and said “at least one of mine has no holes.” • Another boy picked 4 apples similarly. He showed me one of them at random, and it had no holes. He put it back. If you may take just one apple from either boy’s bag, from which boy do you have the better chance of picking an apple without holes?
I don't understand why people are getting into calculations of probability to answer this.
If we assume, as we must, that (i) there are enough apples on the tree for that not to be a factor (ii) the first boy is telling the truth, then: - at least 1/3 of the first boy's apples has no holes; - at least 1/4 of the second boy's apples has no holes. If you can't see that "at least 1/3" is a better chance than "at least 1/4" then that's a bit worrying
I think this is a more complex example of the Monty Hall problem, though. Both sets are altered from random ones by the act of observation.
I don't think it is. In the Monty Hall problem, if we call door 1 the door you picked, then seeing what's behind one other particular door tells you that there is a greater chance than you first assumed that the unpicked unopened door has a car behind it. Here, even though in boy B's case you do get to see a particular apple, you don't get to track that apple so it's not more useful information than merely being told that at least one apple is good.
I think it is because he picked one at random from his 4. That is a more powerful "at least one is good" attribute compared to looking at all 4 and then making the (true) statement.
The remaining 3 remain a random selection unaffected by the removal - assuming it was a tree with many many apples rather than just a small number. Since in the latter case picking one at random that's good means the remainder is biased towards bad - like if you pick a red playing card from a randomly shuffled pack you leave a bias towards black in the remainder.
So I think ProRata has the best answer - you should pick B.
For Boy A you will have the following odds of picking a non-holed apple:
1/3 2/3 3/3
For Boy B it's
1/4 2/4 3/4 4/4
So for Boy A you have a 2/3 chance of having good odds. For Boy B it's only 2/4.
If they really want to upset Banksy, cut out the piece of wall, and auction it to some billionaires.
Everybody knows who he / they are anyway. They have been caught on camera a number of times and I am sure if people can be bothered a bit of a game of follow the money will prove it.
If they really want to upset Banksy, cut out the piece of wall, and auction it to some billionaires.
I think a jury would be reluctant to convict. That would play out either as it not being proved that the mural was "damage" or as accepting an "honestly held belief" that HMCTS or whoever is in charge of the building would have consented to the "damage".
No jury will convict Banksy of criminal damage. If you want to stick it to him, sell his works to people he doesn’t like and use the money for purposes he doesn’t like.
4 apples. 1 definitely good. The remaining 3 each have a 50% chance of being good. So that is an overall probability of 62.5% of picking a good apple from the bag.
Meanwhile for Child A there is only a 50% probability.
If you take it as pure maths and trust that at least 1 of his apples is good, then you've ruled out the permutation where all 3 are bad and left the other 7 permutations where at least one is good.
I think overall that gives you a 12/21 chance of picking a good apple from child A, so about 57%.
Agreeing on the 62.5% on child B, that still, to me, makes B the better bet.
I think you are right on child A but off on child B. Basically, both children have shown the same thing: they have at least one good apple. That rules out the permutation where all apples are bad. That biases the probability of getting a good apple higher, above the basic 50% of the underlying distribution. The size of that bias goes down as the number of apples goes up. With one apple, the bias is worth 50pp: if you know the one apple in the bag is good then your chance of getting a good apple is 100%. With a million apples in the bag, knowing that at least one is good has no effect because the chances of the bag containing no good apples is zero, and so the bias is effectively zero. So you are better off picking from the bag with fewer apples.
No, I'm sticking to mine. The difference, as I see it, is that child A has confirmed "one of my apples" giving the 7 permutations.
Child B has randomly pulled "one specific apple" that now has 100% chance of being good. Let's suspend that at the point where the apple is out of the bag and consider the probabilities on the 3 remaining apples. Still 50/50 for each of them, no, 8 permutations. Now, put the apple back in - nothing changes, that specific apple remains good, not just "one of my apples".
I don't see what difference it makes that Child B has showed you his good apple, as long as Child A's statement can be assumed to be trustworthy. Once Child B puts his apple back in the bag, you're in the same position as Child A but with one more apple. So the maths become:
Child A: 1 in 3 chance of getting the known good apple, 2 in 3 chance of getting one of the others - which have a 50/50 chance of being good - therefore 1 in 3 plus half of 2 in 3 therefore 1 in 3 plus 1 in 3 therefore a 2 in 3 chance of getting a good apple
Child B: 1 in 4 chance of getting the known good apple, 3 in 4 chance of getting one of the others - which have a 50/50 chance of being good - therefore 1 in 4 plus half of 3 in 4 therefore 1 in 4 plus 1.5 in 4 i.e. 3 in 8 therefore 2 in 8 plus 3 in 8 therefore a 5 in 8 chance of getting a good apple
2 in 3 = 67%, 5 in 8 = 62.5% chance. Therefore Child A gives you a better chance of a good apple.
But please carry on trying to convince me that the reverse is true, because I'd love to be wrong on this - I really like counterintuitive statistics.
Thing is, B has picked an apple from his bag of 4 *at random* and it was good. A has looked at all 3 and on that basis has made his "at least one is good" statement. There is a difference there, I think, and ProRata's calc adjusts for this.
What evidence do we have the apple was pulled out at random? I read it as child B showing an apple to demonstrate that at least one apple is good, having seen the full distribution of apples in the bag.
It says that in one of the posts, I think? Otherwise your answer looks right.
If they really want to upset Banksy, cut out the piece of wall, and auction it to some billionaires.
Everybody knows who he / they are anyway. They have been caught on camera a number of times and I am sure if people can be bothered a bit of a game of follow the money will prove it.
If they really want to upset Banksy, cut out the piece of wall, and auction it to some billionaires.
I think a jury would be reluctant to convict. That would play out either as it not being proved that the mural was "damage" or as accepting an "honestly held belief" that HMCTS or whoever is in charge of the building would have consented to the "damage".
Like the mass arrest of the Palestine Acton travel-alongs with placards, it would imo perhaps be best "not to pursue in the public interest". On PA, that would give a nice grey zone leaving them uncertain. Go for the violent ones hard, and the ones who attacked the military - but leave the cannon-fodder alone.
Given Banksy he would probably do one in hot-weather with water-soluble paint, and the Officers could end up with egg-on-face when it ran away a week later.
If they really want to upset Banksy, cut out the piece of wall, and auction it to some billionaires.
Everybody knows who he / they are anyway. They have been caught on camera a number of times and I am sure if people can be bothered a bit of a game of follow the money will prove it.
If they really want to upset Banksy, cut out the piece of wall, and auction it to some billionaires.
I think a jury would be reluctant to convict. That would play out either as it not being proved that the mural was "damage" or as accepting an "honestly held belief" that HMCTS or whoever is in charge of the building would have consented to the "damage".
No jury will convict Banksy of criminal damage. If you want to stick it to him, sell his works to people he doesn’t like and use the money for purposes he doesn’t like.
I would imagine most people would regard removing or painting over the artwork a bigger crime than the creation of it
Although I did rather like the idea of changing the white banner to a St George flag as that would suitably annoy everyone complaining
If they really want to upset Banksy, cut out the piece of wall, and auction it to some billionaires.
Everybody knows who he / they are anyway. They have been caught on camera a number of times and I am sure if people can be bothered a bit of a game of follow the money will prove it.
If they really want to upset Banksy, cut out the piece of wall, and auction it to some billionaires.
I think a jury would be reluctant to convict. That would play out either as it not being proved that the mural was "damage" or as accepting an "honestly held belief" that HMCTS or whoever is in charge of the building would have consented to the "damage".
No jury will convict Banksy of criminal damage. If you want to stick it to him, sell his works to people he doesn’t like and use the money for purposes he doesn’t like.
4 apples. 1 definitely good. The remaining 3 each have a 50% chance of being good. So that is an overall probability of 62.5% of picking a good apple from the bag.
Meanwhile for Child A there is only a 50% probability.
If you take it as pure maths and trust that at least 1 of his apples is good, then you've ruled out the permutation where all 3 are bad and left the other 7 permutations where at least one is good.
I think overall that gives you a 12/21 chance of picking a good apple from child A, so about 57%.
Agreeing on the 62.5% on child B, that still, to me, makes B the better bet.
I think you are right on child A but off on child B. Basically, both children have shown the same thing: they have at least one good apple. That rules out the permutation where all apples are bad. That biases the probability of getting a good apple higher, above the basic 50% of the underlying distribution. The size of that bias goes down as the number of apples goes up. With one apple, the bias is worth 50pp: if you know the one apple in the bag is good then your chance of getting a good apple is 100%. With a million apples in the bag, knowing that at least one is good has no effect because the chances of the bag containing no good apples is zero, and so the bias is effectively zero. So you are better off picking from the bag with fewer apples.
No, I'm sticking to mine. The difference, as I see it, is that child A has confirmed "one of my apples" giving the 7 permutations.
Child B has randomly pulled "one specific apple" that now has 100% chance of being good. Let's suspend that at the point where the apple is out of the bag and consider the probabilities on the 3 remaining apples. Still 50/50 for each of them, no, 8 permutations. Now, put the apple back in - nothing changes, that specific apple remains good, not just "one of my apples".
I don't see what difference it makes that Child B has showed you his good apple, as long as Child A's statement can be assumed to be trustworthy. Once Child B puts his apple back in the bag, you're in the same position as Child A but with one more apple. So the maths become:
Child A: 1 in 3 chance of getting the known good apple, 2 in 3 chance of getting one of the others - which have a 50/50 chance of being good - therefore 1 in 3 plus half of 2 in 3 therefore 1 in 3 plus 1 in 3 therefore a 2 in 3 chance of getting a good apple
Child B: 1 in 4 chance of getting the known good apple, 3 in 4 chance of getting one of the others - which have a 50/50 chance of being good - therefore 1 in 4 plus half of 3 in 4 therefore 1 in 4 plus 1.5 in 4 i.e. 3 in 8 therefore 2 in 8 plus 3 in 8 therefore a 5 in 8 chance of getting a good apple
2 in 3 = 67%, 5 in 8 = 62.5% chance. Therefore Child A gives you a better chance of a good apple.
But please carry on trying to convince me that the reverse is true, because I'd love to be wrong on this - I really like counterintuitive statistics.
Thing is, B has picked an apple from his bag of 4 *at random* and it was good. A has looked at all 3 and on that basis has made his "at least one is good" statement. There is a difference there, I think, and ProRata's calc adjusts for this.
What evidence do we have the apple was pulled out at random? I read it as child B showing an apple to demonstrate that at least one apple is good, having seen the full distribution of apples in the bag.
The Apple Puzzle On a tree, half of the apples have holes made by wasps. • One boy picked 3 apples at random and said “at least one of mine has no holes.” • Another boy picked 4 apples similarly. He showed me one of them at random, and it had no holes. He put it back. If you may take just one apple from either boy’s bag, from which boy do you have the better chance of picking an apple without holes?
Ah then agree, 62.5% for boy B. But that makes it a less interesting puzzle!
Comments
Foolish to make predictions at this early stage, but if it comes down to Thornberry v Phillipson, it'll be Thornberry. Because Labour's membership is mad.
It's all 50/50
Child B has randomly pulled "one specific apple" that now has 100% chance of being good. Let's suspend that at the point where the apple is out of the bag and consider the probabilities on the 3 remaining apples. Still 50/50 for each of them, no, 8 permutations? Now, put the apple back in - nothing changes, that specific apple remains good, not just "one of my apples".
Farage, sadly, has developed bigger ambitions. To win under FPTP you have to present a clear alternative to all others, and be organised in 500-600 seats, and actually try to win in about 450 of them. He has never been in a position to do this before, and he still wouldn't be if Labour had delivered and run stuff brilliantly well.
He can form a government (most seats but not a majority), if he is lucky and we are both unlucky and tactically fail, with about 30% of the vote. Possibly less.
Whereas despite the epic fails of Tory and Labour (so far) the LDs are still in 100 seats absolute max territory.
Genius and luck, momentum optimism and opportunity. Farage will only get one chance. Heaven help the rest of us.
If we assume, as we must, that (i) there are enough apples on the tree for that not to be a factor (ii) the first boy is telling the truth, then:
- at least 1/3 of the first boy's apples has no holes;
- at least 1/4 of the second boy's apples has no holes.
If you can't see that "at least 1/3" is a better chance than "at least 1/4" then that's a bit worrying
The ratio of good to duff decisions by party memberships is pretty awful.
So it’s (100%+50%+50%)/3 in bag A and (100%+50%+50%+50%)/4 in bag B
Which is 66% chance of a good apple in bag A and 62.5% in bag B and as you add more apples the percentage will move closer to the 50% odds you would get from selecting a single apple directly from the tree
Israel has done some monstrous things in recent months, but hitting the HQ of Hamas in Qatar? I’m finding it hard to work up anger
Qatar does some seriously dubious shit
Child A: 1 in 3 chance of getting the known good apple, 2 in 3 chance of getting one of the others - which have a 50/50 chance of being good - therefore 1 in 3 plus half of 2 in 3
therefore 1 in 3 plus 1 in 3
therefore a 2 in 3 chance of getting a good apple
Child B: 1 in 4 chance of getting the known good apple, 3 in 4 chance of getting one of the others - which have a 50/50 chance of being good - therefore 1 in 4 plus half of 3 in 4
therefore 1 in 4 plus 1.5 in 4 i.e. 3 in 8
therefore 2 in 8 plus 3 in 8
therefore a 5 in 8 chance of getting a good apple
2 in 3 = 67%, 5 in 8 = 62.5% chance.
Therefore Child A gives you a better chance of a good apple.
But please carry on trying to convince me that the reverse is true, because I'd love to be wrong on this - I really like counterintuitive statistics.
A gentleman named Elvis is going to escort me from the lounge to my gate, to carry my luggage and ensure I make the flight
He really is called Elvis
If only Israel would restrict herself to surgical strikes like this
NEW: Alison McGovern is joining the deputy leadership contest, saying she wants to fight the "dark forces of right-wing populism".
She says: "I believe I can shape our story, communicating our values in a way that resonates across the Labour family and with the public."
If Mandelson is forced to resign because of documentary evidence that he did something that Trump has also done exactly, then Britain is implicitly making a judgement on Trump's fitness for office.
And vice versa.
By taking one out and putting it back, child B has changed the sample from a random one of four apples to a randomly picked group of three - identical in respect of selection - to child A's, PLUS a good apple.
While child A has told us something about his whole set of three, child B has changed his set to three random choices, plus a known quantity.
Mandelson will have to speak on this. The birthday message is kind of nauseating (like Trump’s). What does he mean by “yum yum”. Is Mandelson referring to the excellent breakfasts Epstein laid on at Lolita island?
Very awkward, at a minimum
Sacking Mandelson would send an explicit message.
Which is why it won't happen, and also why it should.
Both sets are altered from random ones by the act of observation.
Middle East is about to erupt (more)
In both cases, it implies that the membership can be forced to leave their comfort zone, but only after multiple defeats.
I wonder how many Gazans are secretly pleased today
Qatar says it "strongly condemns the cowardly Israeli attack that targeted residential buildings housing several members of the Political Bureau of Hamas ... This criminal assault constitutes a blatant violation of all international laws and norms."
Eliminated:
1 spaces of HHH - left (HNNNN)
The space eliminated is the best possible space for the second child so actually it makes no difference that the first child's bag is better whether we have a large number of apples or a small number assuming replacement or no replacement and even if the underlying probability isn't 50% we're still better off choosing child A (See @Occasionalranter work)
Do we even know that Johnson had not misused his "for public duties" £115k a year? It would be entirely in character for him to misuse it for personal profit.
I'd be looking for a decent enquiry by a Judge, and then a tighter system which is effectively enforced. Boris will squeal Just William style, but sod that - hold the swine to account.
Boris had one enquiry before, which found him to be But because it was a Parliamentary Enquiry he could dodge it by running away:
... when he received the draft of the Commons Privileges Committee investigation into his conduct that unanimously found that he had lied to the Commons on numerous occasions. Johnson resigned his position as MP the same day.
https://en.wikipedia.org/wiki/Boris_Johnson
High risk stuff.
Labour surge
Let the Gazans have peace. Get rid of Hamas
This should go down well in Doha. "US President Donald Trump gave the green light for the Israeli strike in Qatar, a senior Israeli official tells Channel 12."
@John_Hudson
U.S. diplomats in Qatar are sheltering in place following the Israeli strike in Doha and U.S. citizens are advised to do the same, per the US embassy
@reider
Reports in Israel targeted Hamas leadership was meeting to examine Trump's ceasefire proposal. Who would negotiate with the US after this, and the attack on Iran? Death blow to any remaining US credibility in MENA and beyond.
I have seen it suggested Donny should admit to the Epstein letter and try and win the Literature prize instead...
There are 37 sides to the various conflicts and some of them end up with some really, really weird partnerships.
But I’m travelling with a mega posh travel company, writing about them. This is one of the things they do for their customers. It’s like having a butler all the way through the trip - I’ve experienced it before. They are on call 24/7 to do anything you need. Sort your laundry. Book a restaurant. Choose a hike. Probably sexual favours
I can report that Elvis and his friend escorted me all of the 200 yards from the lounge to the gate
Exclusive
Boris Johnson approached Elon Musk on behalf of London Evening Standard owner Lebedev, we can reveal
Former PM’s private office forwarded business proposal from peer to owner of X in June 2024, leaked files suggest
https://x.com/jessicaelgot/status/1965414651510005962
At least 21 civilians were killed and more than two dozen injured following a barbaric direct Russian strike with an air bomb on ordinary people lined up to receive pensions in the village of Yarova in the Donetsk region..
https://x.com/andrii_sybiha/status/1965355437663916266
IMPORTANT: A senior Hamas source told Al Jazeera that the movement’s leadership delegation, headed by Khalil al-Hayya, survived an Israeli assassination attempt carried out through an airstrike in Doha.
https://www.lbc.co.uk/article/banksy-unmasked-police-criminal-damage-5HjdCkY_2/
If they really want to upset Banksy, cut out the piece of wall, and auction it to some billionaires.
That kind of writing deserves something far more... fatal.
Not sure that’s allowable under the ECHR…
Each of the four apples has a 50/50 chance of being good or bad, prior to one of them being checked at random.
After that, three of them still have that 50/50 chance, as they haven't been observed, and the fourth is 100% likely to be good, and is available to be picked again.
That gives you a 62.5% of picking a good apple from the four.
https://docs.google.com/spreadsheets/d/1kPJqGmL_f4jlBboJ17jMv0QBto5nBKvnAxiJRjMz02I/edit?gid=1595646719#gid=1595646719
The remaining 3 remain a random selection unaffected by the removal - assuming it was a tree with many many apples rather than just a small number. Since in the latter case picking one at random that's good means the remainder is biased towards bad - like if you pick a red playing card from a randomly shuffled pack you leave a bias towards black in the remainder.
So I think ProRata has the best answer - you should pick B.
On a tree, half of the apples have holes made by wasps.
• One boy picked 3 apples at random and said “at least one of mine has no holes.”
• Another boy picked 4 apples similarly. He showed me one of them at random, and it had no holes. He put it back.
If you may take just one apple from either boy’s bag, from which boy do you have the better chance of picking an apple without holes?
Just to take one, when the Chief Executive of Warwickshire refused to obey an attempted instruction by the leader of the minority Reform UK group, the minority Council Leader, to take down a flag and informed him of the correct procedure which required consent of the whole Council, his next step was to accuse her of being deliberate Civil Service obstructionism against his aims.
It was BS, but Farage still used it as an example in his conference speech.
Like Trump, they are trying to destroy checks, balances and scrutiny.
I think the poisonous nature of RefUK is out there in letters a mile high.
I'd prefer not to repeatedly call Reform UK politicians liars, but it is what they are.
Update: when I asked a source close to Qatari leadership about them asking Hamas to leave last year, they said “not f*****g like this!”
@annmarie
The number of workers on payrolls will likely be revised down by 911,000 for the 12 months through March — or nearly 76,000 less each month — according to the government’s preliminary benchmark revision.
The final figures are due early next year.
This is a worldwide phenomenon. The UK will not be an exception
1/3 2/3 3/3
For Boy B it's
1/4 2/4 3/4 4/4
So for Boy A you have a 2/3 chance of having good odds. For Boy B it's only 2/4.
So I'd go for Boy A.
Paula Barker has announced on Bluesky she is running for Labour deputy leader
Given Banksy he would probably do one in hot-weather with water-soluble paint, and the Officers could end up with egg-on-face when it ran away a week later.
Although I did rather like the idea of changing the white banner to a St George flag as that would suitably annoy everyone complaining
I'm going to go for another walk this evening