Do the apples identify as good or bad and does the High Court recognise the self ID? That might change the probability a lot. 26.3% chance of a TransGood apple followed by a CisGood one
My apples are INCREDIBLE - some people say they're the most BEAUTIFUL apples they've ever seen! The fake news media won't report it, but EVERYONE knows I have the BEST apples. They should be picking MY apples, not the others. Nobody has apples like this - BELIEVE ME!
The probabilities are fixed when the apples go in the bag but you gain information about the bags. That's the key thing.
The information doesn't change the probabilities. That's the key thing.
Which would be fine if the bags were not restricted. But they are. Just because bag a is three random apples, doesn't mean that follows later. The statistics of what you see depend on the evidence you are given.
Nope
Your odds of throwing a 6 don't increase just cos I show you that side of a die
Consider the situation with two apples. Four different bags are GG, GB, BG, BB. If you see an apple from a bag that is G that bag cannot be BB. Therefore it's one of the GG, BG or GB. So your random apple is now 4/6 chance of being G.
The freedom flotilla drone attack is my favourite story of the day
It seems very clearly to me to be a self-inflicted flare attack
A great example of how an untruth can go around the world before it’s clearly proven to be wrong.
As opposed to the murder of Iryna Zarutska, where the media totallly ignored a cold-blooded and unprovoked killing that took place in public, because it didn’t fit their preferred ‘narrative’’.
It's all over the media now.
Sadly with, in the US at least, some terrible headlines about how drawing attention to these events plays into Trump’s hands about violent crime in cities, and how widespread CCTV “leaks” risk social unrest.
Rather than how someone can be arrested 14 times for violent offences and still be out on the streets.
The probabilities are fixed when the apples go in the bag but you gain information about the bags. That's the key thing.
The information doesn't change the probabilities. That's the key thing.
Which would be fine if the bags were not restricted. But they are. Just because bag a is three random apples, doesn't mean that follows later. The statistics of what you see depend on the evidence you are given.
Nope
Your odds of throwing a 6 don't increase just cos I show you that side of a die
That's not an apt comparison.
It really is
The whole point is that the information you are given about the contents of the bags doesn't change the probabilities inside the bag.
Showing you the dice doesn't change the odds.
Not if the dice is going to be re-rolled, no, because then it can change.
But if its locked into being a six, as it won't be re-rolled, then yes of course it changes the odds. If I say bag A has 3 dice, one of which I can see is showing a 6 then of course the odds change over not knowing beforehand.
The set of possible outcomes has changed as soon as you acquired new information.
A good apple is locked into being a good apple, it won't magically become bad or spoil.
I just saw Concorde. Didn’t know they keep one at Heathrow. But so it is
Kinda poignant
And STILL beautiful
Concorde is proof we were more advance in the 60/70s than we are today.
Utterly incorrect. We have the science and technology to build a Concorde replacement, or something better than Concorde, today.
What we don't have is an economic market for such a plane.
There was barely an economic market for Concorde at the time. London/Paris to New York was the only one that airlines ever found, and I'm not sure about Paris.
And now we have video calls, which do a decent percentage of what Concorde did for a tiny fraction of the cost.
Progress sometimes looks odd.
Concorde and its American oppos were supposed to be the mass market and the 747 was an interim design made to be easily convertible to freight loading when the self-loading cargo all marched off to go on Concorde and the Boeing 2707.
instead it ended up being close to a classic Veblenian luxury item (how close depends how seriously one can take the argument about nipping over to NYC for a quick head to head by captains of industry and bacl in time for dinner).
BA famously did a survey of their scheduled Concorde customers, those actually on the plane, asking them how much they thought their own ticket had cost.
They way overestimated the actual price, so BA doubled the price of scheduled LHR<>JFK Concorde tickets.
A tiny percentage had actually booked it themselves, most being booked by PAs and on behalf of others via agents and management companies.
Do the apples identify as good or bad and does the High Court recognise the self ID? That might change the probability a lot. 26.3% chance of a TransGood apple followed by a CisGood one
My apples are INCREDIBLE - some people say they're the most BEAUTIFUL apples they've ever seen! The fake news media won't report it, but EVERYONE knows I have the BEST apples. They should be picking MY apples, not the others. Nobody has apples like this - BELIEVE ME!
Thank you for your attention to this matter.
I grew up in a council tree in a rough part of the orchard. We didn't have much but we were happy apples. The other apples would rally round if a maggot got in. Thats community. Something Thatcher apples destroyed.
The Lib Dem’s are taking a leaf out of Norman Tebbit’s book in the eighties and pressuring the state broadcaster over its coverage for Reform making it clear the BBC needs to reduce covering them. They’ve just had their party conference for goodness sake.
I also cannot see how this does them any favours or harms Reform. It simply plays into the Reform claim of being an insurgent the main parties all oppose.
Pathetic party.
Absolutely no opposition to this ghastly Government, rather wail about a fellow opposition party. Dereliction of duty.
They’re doubling down on it too. They probably are crying for attention as their conference is probably imminent.
I don’t know why Twitter is spamming the piss diamonds twitter feed into my timeline.
The probabilities are fixed when the apples go in the bag but you gain information about the bags. That's the key thing.
The information doesn't change the probabilities. That's the key thing.
Which would be fine if the bags were not restricted. But they are. Just because bag a is three random apples, doesn't mean that follows later. The statistics of what you see depend on the evidence you are given.
Nope
Your odds of throwing a 6 don't increase just cos I show you that side of a die
That's not an apt comparison.
It really is
The whole point is that the information you are given about the contents of the bags doesn't change the probabilities inside the bag.
Showing you the dice doesn't change the odds.
Ok one last try ...
Imagine you ONE THOUSAND times pick an apple at random from the bag of 4 and every single time it's a good one.
Are you saying this does not change the probabilities of what's inside that bag very strongly in favour of all 4 apples being good?
Course it does. C'mon.
Flipping a coin heads 100 times doesn't change the odds of the next throw.
The odds in the bag are fixed. They don't change no matter how often you pick right. Any right pick doesn't change the odds of the next pick.
But you don't have 1000 picks
There are 2 bags. The odds in each bag are fixed. Which bag do you pick?
I just saw Concorde. Didn’t know they keep one at Heathrow. But so it is
Kinda poignant
And STILL beautiful
Concorde is proof we were more advance in the 60/70s than we are today.
Utterly incorrect. We have the science and technology to build a Concorde replacement, or something better than Concorde, today.
What we don't have is an economic market for such a plane.
There was barely an economic market for Concorde at the time. London/Paris to New York was the only one that airlines ever found, and I'm not sure about Paris.
And now we have video calls, which do a decent percentage of what Concorde did for a tiny fraction of the cost.
Progress sometimes looks odd.
Concorde and its American oppos were supposed to be the mass market and the 747 was an interim design made to be easily convertible to freight loading when the self-loading cargo all marched off to go on Concorde and the Boeing 2707.
instead it ended up being close to a classic Veblenian luxury item (how close depends how seriously one can take the argument about nipping over to NYC for a quick head to head by captains of industry and bacl in time for dinner).
It is said, though I do not know how accurately, that American opposition to sonic booms over land became a crucial factor just after Boeing abandoned its own efforts to build a supersonic airliner.
I just saw Concorde. Didn’t know they keep one at Heathrow. But so it is
Kinda poignant
And STILL beautiful
Concorde is proof we were more advance in the 60/70s than we are today.
Utterly incorrect. We have the science and technology to build a Concorde replacement, or something better than Concorde, today.
What we don't have is an economic market for such a plane.
There was barely an economic market for Concorde at the time. London/Paris to New York was the only one that airlines ever found, and I'm not sure about Paris.
And now we have video calls, which do a decent percentage of what Concorde did for a tiny fraction of the cost.
Progress sometimes looks odd.
Concorde and its American oppos were supposed to be the mass market and the 747 was an interim design made to be easily convertible to freight loading when the self-loading cargo all marched off to go on Concorde and the Boeing 2707.
instead it ended up being close to a classic Veblenian luxury item (how close depends how seriously one can take the argument about nipping over to NYC for a quick head to head by captains of industry and bacl in time for dinner).
BA famously did a survey of their customers, asking them how much they thought their own ticket had cost. They way overestimated the actual price, so BA doubled the price of scheduled LHR<>JFK Concorde tickets. A tiny percentage had actually booked it themselves, most being booked by PAs and on behalf of others via agents and management companies.
Two triumphs of engineering kept Concorde flying as long as it did. One was the aeronautics that built it. The other was the financial engineering around the time BA was privatised that kept it going.
(The TLDR is something like- if the costs to date are written off, it only has to fly a couple of hours a day, unlike an easyJet Airbus now. Then you can fly full with a small number of people paying top whack for decent cheese and wine. And then the costs work. There's a brilliant telling of the tale in Francis Spufford's book, Backroom Boys.)
Consider the situation with two apples. Four different bags are GG, GB, BG, BB. If you see an apple from a bag that is G that bag cannot be BB. Therefore it's one of the GG, BG or GB. So your random apple is now 4/6 chance of being G.
Ummm, that's the point. Your odds have not changed because you already have the information when you start.
Let's try this
1 bag with 1 apple. You know 1 apple is good. What are your odds of picking a good apple from that bag?
1 bag with 2 apples. You know 1 apple is good. What are your odds of picking a good apple from that bag?
1 bag with 3 apples. You know 1 apple is good. What are your odds of picking a good apple from that bag?
1 bag with 4 apples. You know 1 apple is good. What are your odds of picking a good apple from that bag?
The original question is about comparative odds between the bags. The odds don't change during the game.
Knowing 1 apple is good changes the comparative odds between the bags at the start of the game, but doesn't change the odds for any given bag during the game.
The probabilities are fixed when the apples go in the bag but you gain information about the bags. That's the key thing.
The information doesn't change the probabilities. That's the key thing.
Which would be fine if the bags were not restricted. But they are. Just because bag a is three random apples, doesn't mean that follows later. The statistics of what you see depend on the evidence you are given.
Nope
Your odds of throwing a 6 don't increase just cos I show you that side of a die
That's not an apt comparison.
It really is
The whole point is that the information you are given about the contents of the bags doesn't change the probabilities inside the bag.
Showing you the dice doesn't change the odds.
Ok one last try ...
Imagine you ONE THOUSAND times pick an apple at random from the bag of 4 and every single time it's a good one.
Are you saying this does not change the probabilities of what's inside that bag very strongly in favour of all 4 apples being good?
Course it does. C'mon.
Flipping a coin heads 100 times doesn't change the odds of the next throw.
The odds in the bag are fixed. They don't change no matter how often you pick right. Any right pick doesn't change the odds of the next pick.
But you don't have 1000 picks
There are 2 bags. The odds in each bag are fixed. Which bag do you pick?
The bag about which you have most information. This is the one with three apples, at least one of which is good. For the reasons explained above.
The probabilities are fixed when the apples go in the bag but you gain information about the bags. That's the key thing.
The information doesn't change the probabilities. That's the key thing.
But it does!
Eg what if, faced with the bag of 4, you FIVE times select an apple at random (before putting it back) and every time it's a good one.
Is this going to impact your assessment of the mix of apples in that bag?
Of course it is. You'll decide (rightly) that they are probably mainly good.
Yes, but IT DOESN'T CHANGE THE PROBABILITY
IT DOES. Having done 5 random draws of a good apple you are armed with information telling you that the probability of picking a good apple from that bag is very high.
This is not like red/black in roulette or a dice.
It really is
You seem to be arguing that playing Russian Roulette and not getting shot 5 times makes it less likely you will get shot on the 6th attempt...
And remember the original problem is which of 2 bags would you pick.
You know both of them have at least 1 good apple, but knowing that doesn't make 1 bag better than the other
The difference is that with the three apple bag the information about at least one good apple is imparted after a view of all the apples, whereas for the four apple bag an apple is chosen at random and happens to be good. This increases the probability that the majority of the apples in this bag are good, because if only one out of four was good you would be less likely to have pulled a good apple out of it.
The probabilities are fixed when the apples go in the bag but you gain information about the bags. That's the key thing.
The information doesn't change the probabilities. That's the key thing.
Which would be fine if the bags were not restricted. But they are. Just because bag a is three random apples, doesn't mean that follows later. The statistics of what you see depend on the evidence you are given.
Nope
Your odds of throwing a 6 don't increase just cos I show you that side of a die
That's not an apt comparison.
It really is
The whole point is that the information you are given about the contents of the bags doesn't change the probabilities inside the bag.
Showing you the dice doesn't change the odds.
Ok one last try ...
Imagine you ONE THOUSAND times pick an apple at random from the bag of 4 and every single time it's a good one.
Are you saying this does not change the probabilities of what's inside that bag very strongly in favour of all 4 apples being good?
Course it does. C'mon.
Flipping a coin heads 100 times doesn't change the odds of the next throw.
The odds in the bag are fixed. They don't change no matter how often you pick right. Any right pick doesn't change the odds of the next pick.
But you don't have 1000 picks
There are 2 bags. The odds in each bag are fixed. Which bag do you pick?
If you had two bags both with four apples, and you were told bag A had at least one good apple, you would surely pick bag A as you’ve eliminated the option of them all being bad.
The probabilities are fixed when the apples go in the bag but you gain information about the bags. That's the key thing.
The information doesn't change the probabilities. That's the key thing.
Which would be fine if the bags were not restricted. But they are. Just because bag a is three random apples, doesn't mean that follows later. The statistics of what you see depend on the evidence you are given.
Nope
Your odds of throwing a 6 don't increase just cos I show you that side of a die
That's not an apt comparison.
It really is
The whole point is that the information you are given about the contents of the bags doesn't change the probabilities inside the bag.
Showing you the dice doesn't change the odds.
Ok one last try ...
Imagine you ONE THOUSAND times pick an apple at random from the bag of 4 and every single time it's a good one.
Are you saying this does not change the probabilities of what's inside that bag very strongly in favour of all 4 apples being good?
Course it does. C'mon.
Flipping a coin heads 100 times doesn't change the odds of the next throw.
The odds in the bag are fixed. They don't change no matter how often you pick right. Any right pick doesn't change the odds of the next pick.
But you don't have 1000 picks
There are 2 bags. The odds in each bag are fixed. Which bag do you pick?
It's a shame someone hasn't posted the correct solution on bluesky. Scott wouldn't have had any trouble accepting it was true then.
I just saw Concorde. Didn’t know they keep one at Heathrow. But so it is
Kinda poignant
And STILL beautiful
Concorde is proof we were more advance in the 60/70s than we are today.
Utterly incorrect. We have the science and technology to build a Concorde replacement, or something better than Concorde, today.
What we don't have is an economic market for such a plane.
There was barely an economic market for Concorde at the time. London/Paris to New York was the only one that airlines ever found, and I'm not sure about Paris.
And now we have video calls, which do a decent percentage of what Concorde did for a tiny fraction of the cost.
Progress sometimes looks odd.
Concorde and its American oppos were supposed to be the mass market and the 747 was an interim design made to be easily convertible to freight loading when the self-loading cargo all marched off to go on Concorde and the Boeing 2707.
instead it ended up being close to a classic Veblenian luxury item (how close depends how seriously one can take the argument about nipping over to NYC for a quick head to head by captains of industry and bacl in time for dinner).
BA famously did a survey of their customers, asking them how much they thought their own ticket had cost. They way overestimated the actual price, so BA doubled the price of scheduled LHR<>JFK Concorde tickets. A tiny percentage had actually booked it themselves, most being booked by PAs and on behalf of others via agents and management companies.
Two triumphs of engineering kept Concorde flying as long as it did. One was the aeronautics that built it. The other was the financial engineering around the time BA was privatised that kept it going.
(The TLDR is something like- if the costs to date are written off, it only has to fly a couple of hours a day, unlike an easyJet Airbus now. Then you can fly full with a small number of people paying top whack for decent cheese and wine. And then the costs work. There's a brilliant telling of the tale in Francis Spufford's book, Backroom Boys.)
The probabilities are fixed when the apples go in the bag but you gain information about the bags. That's the key thing.
The information doesn't change the probabilities. That's the key thing.
Which would be fine if the bags were not restricted. But they are. Just because bag a is three random apples, doesn't mean that follows later. The statistics of what you see depend on the evidence you are given.
Nope
Your odds of throwing a 6 don't increase just cos I show you that side of a die
That's not an apt comparison.
It really is
The whole point is that the information you are given about the contents of the bags doesn't change the probabilities inside the bag.
Showing you the dice doesn't change the odds.
Ok one last try ...
Imagine you ONE THOUSAND times pick an apple at random from the bag of 4 and every single time it's a good one.
Are you saying this does not change the probabilities of what's inside that bag very strongly in favour of all 4 apples being good?
Course it does. C'mon.
Flipping a coin heads 100 times doesn't change the odds of the next throw.
The odds in the bag are fixed. They don't change no matter how often you pick right. Any right pick doesn't change the odds of the next pick.
But you don't have 1000 picks
There are 2 bags. The odds in each bag are fixed. Which bag do you pick?
Flipping heads 100 times in a row might not alter the odds of the next throw but it really should make you question whether the coin is fair.
The probabilities are fixed when the apples go in the bag but you gain information about the bags. That's the key thing.
The information doesn't change the probabilities. That's the key thing.
Which would be fine if the bags were not restricted. But they are. Just because bag a is three random apples, doesn't mean that follows later. The statistics of what you see depend on the evidence you are given.
Nope
Your odds of throwing a 6 don't increase just cos I show you that side of a die
That's not an apt comparison.
It really is
The whole point is that the information you are given about the contents of the bags doesn't change the probabilities inside the bag.
Showing you the dice doesn't change the odds.
Ok one last try ...
Imagine you ONE THOUSAND times pick an apple at random from the bag of 4 and every single time it's a good one.
Are you saying this does not change the probabilities of what's inside that bag very strongly in favour of all 4 apples being good?
Course it does. C'mon.
Flipping a coin heads 100 times doesn't change the odds of the next throw.
The odds in the bag are fixed. They don't change no matter how often you pick right. Any right pick doesn't change the odds of the next pick.
But you don't have 1000 picks
There are 2 bags. The odds in each bag are fixed. Which bag do you pick?
You're talking about new events though.
Let's take a coin, it could be heads or tails. I show a heads, next time it could be tails.
On the other hand if I take a coin out of the bag and show you both sides of the coin are heads, it's a double-headed trick coin, does that change the odds? Of course it does!
The apple is the same. Before the reveal it was a normal coin, could be heads, could be tails, could be good, could be bad, no way of knowing so it was 50%
After the reveal you know. So its no longer 50%, if you get the apple it is 100% definitely going to be good, its state can't change.
Consider the situation with two apples. Four different bags are GG, GB, BG, BB. If you see an apple from a bag that is G that bag cannot be BB. Therefore it's one of the GG, BG or GB. So your random apple is now 4/6 chance of being G.
Ummm, that's the point. Your odds have not changed because you already have the information when you start.
Let's try this
1 bag with 1 apple. You know 1 apple is good. What are your odds of picking a good apple from that bag?
1 bag with 2 apples. You know 1 apple is good. What are your odds of picking a good apple from that bag?
1 bag with 3 apples. You know 1 apple is good. What are your odds of picking a good apple from that bag?
1 bag with 4 apples. You know 1 apple is good. What are your odds of picking a good apple from that bag?
The original question is about comparative odds between the bags. The odds don't change during the game.
Knowing 1 apple is good changes the comparative odds between the bags at the start of the game, but doesn't change the odds for any given bag during the game.
The start of the game is irrelevant. You don't know what is in the bag beyond the information supplied. If there were a bunch of random three apple bags at least a few would have all bad apples. But we know that our bag is not one of them, so the remaining chances suggest a random apple is more likely good than bad, and better odds the fewer apples there are, as the effect is bigger. And on that if you can't be persuaded, I'm back to knitting and watching a 0-0 draw...
It's taken three years to recover from China hack, election watchdog says
The UK's elections watchdog says it's taken three years and at least a quarter of a million pounds to fully recover from a hack that saw the private details of 40m voters accessed by Chinese cyber spies. https://www.bbc.co.uk/news/articles/c80gl8yvj9go
The probabilities are fixed when the apples go in the bag but you gain information about the bags. That's the key thing.
The information doesn't change the probabilities. That's the key thing.
Which would be fine if the bags were not restricted. But they are. Just because bag a is three random apples, doesn't mean that follows later. The statistics of what you see depend on the evidence you are given.
Nope
Your odds of throwing a 6 don't increase just cos I show you that side of a die
That's not an apt comparison.
It really is
The whole point is that the information you are given about the contents of the bags doesn't change the probabilities inside the bag.
Showing you the dice doesn't change the odds.
Ok one last try ...
Imagine you ONE THOUSAND times pick an apple at random from the bag of 4 and every single time it's a good one.
Are you saying this does not change the probabilities of what's inside that bag very strongly in favour of all 4 apples being good?
Course it does. C'mon.
Flipping a coin heads 100 times doesn't change the odds of the next throw.
The odds in the bag are fixed. They don't change no matter how often you pick right. Any right pick doesn't change the odds of the next pick.
But you don't have 1000 picks
There are 2 bags. The odds in each bag are fixed. Which bag do you pick?
No, the choice of apples in the bag is fixed. But you don't know what it is, only that each apple had a 50/50 chance of being one thing or the other.
By picking one out, and finding it's a good one, you have changed your knowledge. Every other apple still has a 50/50 chance of being either good or bad.
The probabilities are fixed when the apples go in the bag but you gain information about the bags. That's the key thing.
The information doesn't change the probabilities. That's the key thing.
Which would be fine if the bags were not restricted. But they are. Just because bag a is three random apples, doesn't mean that follows later. The statistics of what you see depend on the evidence you are given.
Nope
Your odds of throwing a 6 don't increase just cos I show you that side of a die
That's not an apt comparison.
It really is
The whole point is that the information you are given about the contents of the bags doesn't change the probabilities inside the bag.
Showing you the dice doesn't change the odds.
Ok one last try ...
Imagine you ONE THOUSAND times pick an apple at random from the bag of 4 and every single time it's a good one.
Are you saying this does not change the probabilities of what's inside that bag very strongly in favour of all 4 apples being good?
Course it does. C'mon.
Flipping a coin heads 100 times doesn't change the odds of the next throw.
The odds in the bag are fixed. They don't change no matter how often you pick right. Any right pick doesn't change the odds of the next pick.
But you don't have 1000 picks
There are 2 bags. The odds in each bag are fixed. Which bag do you pick?
The coin is getting re-tossed each time and it's always 50/50. So each toss tells you nothing about the next one. Assuming not bent of course. Same with dice and roulette.
This otoh is a fixed bag of apples. It's not being reassembled after each random pick and replace. Therefore each random pick and replace does tell you something about its contents. And the more you do the more it tells you.
The probabilities are fixed when the apples go in the bag but you gain information about the bags. That's the key thing.
The information doesn't change the probabilities. That's the key thing.
Which would be fine if the bags were not restricted. But they are. Just because bag a is three random apples, doesn't mean that follows later. The statistics of what you see depend on the evidence you are given.
Nope
Your odds of throwing a 6 don't increase just cos I show you that side of a die
That's not an apt comparison.
It really is
The whole point is that the information you are given about the contents of the bags doesn't change the probabilities inside the bag.
Showing you the dice doesn't change the odds.
Ok one last try ...
Imagine you ONE THOUSAND times pick an apple at random from the bag of 4 and every single time it's a good one.
Are you saying this does not change the probabilities of what's inside that bag very strongly in favour of all 4 apples being good?
Course it does. C'mon.
Flipping a coin heads 100 times doesn't change the odds of the next throw.
The odds in the bag are fixed. They don't change no matter how often you pick right. Any right pick doesn't change the odds of the next pick.
But you don't have 1000 picks
There are 2 bags. The odds in each bag are fixed. Which bag do you pick?
We know that the odds for a fair coin are 50:50, but we don't know what the odds are for each of these bags. We don't know how many good or bad apples are in each.
The fact that a good one is pulled out of one the bags at random gives us a bit of information about the content of that bag. It makes a distribution of three good apples/one bad apple slightly more likely than one good apple/three bad apples, whereas before you pulled the good apple out those distributions would have been equally likely.
Plenty of ways you can look at the voting intention of 16-17 year olds, but here's a fun one:
➡️ PE and Business Studies students are much more likely to vote Reform 🌍 The Green Party does best with those who enjoy Drama at school 🔶 Lib Dems do best with modern language fans https://x.com/edhodgsoned/status/1965428390732976179
Uh oh.
PE and Business Studies.
Tories meanwhile do best amongst those who loved Maths, like Rishi and Geography. Labour do best amongst those who liked English then Maths best
We do appreciate of course that these are just for a bit of fun and are based on tiny subsamples. No more accurate than VI by biscuit choice
Royalists like Bourbons.
While Republicans go for Garibaldi's.
Andrea Jenkyns is partial to a Lincoln biscuit
I would think something half baked would be the Reform choice.
Or a biscuit made from distilled rage and bits of flag
Or perhaps a Madeline in Remembrance of Things Past.
The probabilities are fixed when the apples go in the bag but you gain information about the bags. That's the key thing.
The information doesn't change the probabilities. That's the key thing.
Which would be fine if the bags were not restricted. But they are. Just because bag a is three random apples, doesn't mean that follows later. The statistics of what you see depend on the evidence you are given.
Nope
Your odds of throwing a 6 don't increase just cos I show you that side of a die
That's not an apt comparison.
It really is
The whole point is that the information you are given about the contents of the bags doesn't change the probabilities inside the bag.
Showing you the dice doesn't change the odds.
Ok one last try ...
Imagine you ONE THOUSAND times pick an apple at random from the bag of 4 and every single time it's a good one.
Are you saying this does not change the probabilities of what's inside that bag very strongly in favour of all 4 apples being good?
Course it does. C'mon.
Flipping a coin heads 100 times doesn't change the odds of the next throw.
The odds in the bag are fixed. They don't change no matter how often you pick right. Any right pick doesn't change the odds of the next pick.
But you don't have 1000 picks
There are 2 bags. The odds in each bag are fixed. Which bag do you pick?
Flipping heads 100 times in a row might not alter the odds of the next throw but it really should make you question whether the coin is fair.
Obligitary video of Derren Brown flipping a fair coin heads 10 times in a row.
Yes it’s a totally genuine film, doesn’t cut away and the coin is a real coin.
You’re watching the last minute of a 10-hour long video. Derren Brown is the guy who’s crazy enough to know that if you keep going it will happen eventually.
The fact of it being chosen at random and being good changes (towards good) the probability distribution of the population of 4.
No it doesn't
It does.
nope
Imagine a bag containing 4 balls. Each ball has a 50% chance of being white or black
What are your odds of selecting a white ball?
I select a white ball and show it to you and put it back.
What are your odds of selecting a white ball?
They haven't changed between your 2 attempts...
Don't bite me if wrong
Before you show: 50% (50+50+50+50/4) After you show: 62.5% (100+50+50+50/4)
It greatly depends if the white one was chosen at random or not.
If the person doing the reveal can choose the white one (as long as any are present) that greatly reduces the information you've gained.
If they can select any white, if any exist, then you are only eliminating the 4 blacks outcome. If the 1st one is black they pick the 2nd and show it if its white, if that's black they show the third if its white, etc
If a random one has been chosen and it happened to be black, you're eliminating all the possible outcomes for that ball. They're showing you the 1st one so you know more now.
We know that the odds for a fair coin are 50:50, but we don't know what the odds are for each of these bags. We don't know how many good or bad apples are in each.
We don't know the distribution, but we absolutely know the odds.
We can calculate the odds for each bag, and pick the best one.
"Opinion Outlook The ‘lanyard class’ of Brussels It’s a sign of the times that something once used to keep knives secure now carries an official name card Alice Hancock" (£)
My son brought a waif home after school today, another boy in his year. I let the boy's mother he was here, then offered him a simple dinner of chicken and rice.
He is twelve.
It was the first time he had ever had rice.
I was flabbergasted.
I was 18 before I had rice
When I was a kid, every week my mum would cook some concoction with lentils in it.
As a result, I *never* cook with lentils...
As for rice: it is simple to cook, but easy to muck up. We do it the Turkish way: fry some orzo in butter before adding the rice and water.
I like lentils tbf, and split peas. Nice bit of pease pudding. Mum was an extremely traditional English cook - and a little of thrift dishes as we weren't ever so well off. Leftover meals, bubble and squeak etc etc and plenty Yorkshires to fill you up with roasts. Suet pudding of savory and sweet kinds, proper Norfolk dumplings and simple sinkers too. Yum. But baking was where my mums family all excelled and excel, my great grandma was in service to the local big families (Gurneys etc), a senior member of various kitchens and through her the female members of my clan all bake like its second nature. As do I now tbf
You’re making me nostalgic. My maternal grandmother was in service at Blickling Hall. She was sent there after her mother, stepfather and sister all died in the last outbreak of Bubonic Plague in England. Near Ipswich in 1910.
This otoh is a fixed bag of apples. It's not being reassembled after each random pick and replace. Therefore each random pick and replace does tell you something about its contents. And the more you do the more it tells you.
That's the essential difference.
But you only do it once for each bag so you don't learn any more.
The amount of information is fixed at the start of the game.
We know that the odds for a fair coin are 50:50, but we don't know what the odds are for each of these bags. We don't know how many good or bad apples are in each.
We don't know the distribution, but we absolutely know the odds.
We can calculate the odds for each bag, and pick the best one.
Yes and the odds aren't the same for each bag, because the set of possible outcomes was changed by the reveal.
Since the set of possible outcomes is the denominator for any probability question, changing the denominator changes the probability.
The probabilities are fixed when the apples go in the bag but you gain information about the bags. That's the key thing.
The information doesn't change the probabilities. That's the key thing.
Which would be fine if the bags were not restricted. But they are. Just because bag a is three random apples, doesn't mean that follows later. The statistics of what you see depend on the evidence you are given.
Nope
Your odds of throwing a 6 don't increase just cos I show you that side of a die
That's not an apt comparison.
It really is
The whole point is that the information you are given about the contents of the bags doesn't change the probabilities inside the bag.
Showing you the dice doesn't change the odds.
Ok one last try ...
Imagine you ONE THOUSAND times pick an apple at random from the bag of 4 and every single time it's a good one.
Are you saying this does not change the probabilities of what's inside that bag very strongly in favour of all 4 apples being good?
Course it does. C'mon.
Are you lot still going on about apples? Why not do something useful and give them to @wooliedyed to make a pie.
This otoh is a fixed bag of apples. It's not being reassembled after each random pick and replace. Therefore each random pick and replace does tell you something about its contents. And the more you do the more it tells you.
That's the essential difference.
But you only do it once for each bag so you don't learn any more.
The amount of information is fixed at the start of the game.
No, the reveal changed the information. It gave you new information.
Prior to the reveal, the bag could have had all bad apples, after the reveal it can't. Different set of possible outcomes, therefore different odds.
Do the apples identify as good or bad and does the High Court recognise the self ID? That might change the probability a lot. 26.3% chance of a TransGood apple followed by a CisGood one
My apples are INCREDIBLE - some people say they're the most BEAUTIFUL apples they've ever seen! The fake news media won't report it, but EVERYONE knows I have the BEST apples. They should be picking MY apples, not the others. Nobody has apples like this - BELIEVE ME!
Thank you for your attention to this matter.
I grew up in a council tree in a rough part of the orchard. We didn't have much but we were happy apples. The other apples would rally round if a maggot got in. Thats community. Something Thatcher apples destroyed.
My son brought a waif home after school today, another boy in his year. I let the boy's mother he was here, then offered him a simple dinner of chicken and rice.
He is twelve.
It was the first time he had ever had rice.
I was flabbergasted.
I was 18 before I had rice
When I was a kid, every week my mum would cook some concoction with lentils in it.
As a result, I *never* cook with lentils...
As for rice: it is simple to cook, but easy to muck up. We do it the Turkish way: fry some orzo in butter before adding the rice and water.
I like lentils tbf, and split peas. Nice bit of pease pudding. Mum was an extremely traditional English cook - and a little of thrift dishes as we weren't ever so well off. Leftover meals, bubble and squeak etc etc and plenty Yorkshires to fill you up with roasts. Suet pudding of savory and sweet kinds, proper Norfolk dumplings and simple sinkers too. Yum. But baking was where my mums family all excelled and excel, my great grandma was in service to the local big families (Gurneys etc), a senior member of various kitchens and through her the female members of my clan all bake like its second nature. As do I now tbf
You’re making me nostalgic. My maternal grandmother was in service at Blickling Hall. She was sent there after her mother, stepfather and sister all died in the last outbreak of Bubonic Plague in England. Near Ipswich in 1910.
Great Nanny would have been in Service at the same time. She lived to be 101 so i got to meet her as a mini Woolie
The probabilities are fixed when the apples go in the bag but you gain information about the bags. That's the key thing.
The information doesn't change the probabilities. That's the key thing.
Which would be fine if the bags were not restricted. But they are. Just because bag a is three random apples, doesn't mean that follows later. The statistics of what you see depend on the evidence you are given.
Nope
Your odds of throwing a 6 don't increase just cos I show you that side of a die
That's not an apt comparison.
It really is
The whole point is that the information you are given about the contents of the bags doesn't change the probabilities inside the bag.
Showing you the dice doesn't change the odds.
Ok one last try ...
Imagine you ONE THOUSAND times pick an apple at random from the bag of 4 and every single time it's a good one.
Are you saying this does not change the probabilities of what's inside that bag very strongly in favour of all 4 apples being good?
Course it does. C'mon.
Are you lot still going on about apples? Why not do something useful and give them to @wooliedyed to make a pie.
The freedom flotilla drone attack is my favourite story of the day
It seems very clearly to me to be a self-inflicted flare attack
A great example of how an untruth can go around the world before it’s clearly proven to be wrong.
As opposed to the murder of Iryna Zarutska, where the media totallly ignored a cold-blooded and unprovoked killing that took place in public, because it didn’t fit their preferred ‘narrative’’.
It's all over the media now.
Sadly with, in the US at least, some terrible headlines about how drawing attention to these events plays into Trump’s hands about violent crime in cities, and how widespread CCTV “leaks” risk social unrest.
Rather than how someone can be arrested 14 times for violent offences and still be out on the streets.
Was he convicted of any? If not, the number of arrests is irrelevant.
One of the paradoxes of extremely harsh sentences is that juries become reluctant to convict.
It appears that the man was homeless and severely schizophrenic, with a number of pending cases for violent acts, but he was continually bailed pending court apprearances for which he didn’t show.
Which is why it’s a very political case, it illustrates just how crazy some of the cities in the US have got when it comes to crime. The mayor of Charlotte made a very generic statement about mental health and homelessness, without any reference to the victim of the murder. https://x.com/libsoftiktok/status/1964739505912762785
Without wishing to go all @Leon, this case is a potential breaking point in race relations in the US.
The odds of picking a good apple from either bag don't change based on the information presented.
Again, if I pick an apple from either bag and show it to you, when I put it back your odds of picking a good apple have not changed.
This is where it differs from the Monty Hall problem where 1 door is eliminated.
In this game the odds are fixed, and don't change. Both boys got lucky.
The question for you is, do you feel lucky? Well, do ya punk?
The plausible combinations outside the bag gives you the odds. picking blindfolded from the tree odds are 50/50.
From bag A the odds are 66%, bag B 62.5% were there bag C with 1 known and 4 unknown 60%, bag alpha with 1 known and 1 unknown 75%.
Basically no matter how you phrase the question there is a bag with 1 good apple and x-1 apples of unknown status in it the odds of picking a good apple is x+1/2x where x is the number of apples in the bag
The context of the question being posed, that of how to evaluate data that forms opinion polling, especially allocating don't knows and certain to votes, surely leads us to the answer being one of trust rather than mathematics?
That's why I plumped for B anyway, that child showed us a good apple, the other one just told us he had some
This otoh is a fixed bag of apples. It's not being reassembled after each random pick and replace. Therefore each random pick and replace does tell you something about its contents. And the more you do the more it tells you.
That's the essential difference.
But you only do it once for each bag so you don't learn any more.
The amount of information is fixed at the start of the game.
The two scenarios are different.
In one, you have information about the bag as a whole.
In the other, you have information about a specific apple.
I ran through all the possibilities in the other thread.
57% and 62.5%
Feel free to code it up and run a Monte Carlo simulation.
Lets see if our pathetic Prime Minister can raise is game tomorrow from pathetic to luke warm and show this sort of spirit. Otherwise the party will boot him out.
The odds of picking a good apple from either bag don't change based on the information presented.
Again, if I pick an apple from either bag and show it to you, when I put it back your odds of picking a good apple have not changed.
This is where it differs from the Monty Hall problem where 1 door is eliminated.
In this game the odds are fixed, and don't change. Both boys got lucky.
The question for you is, do you feel lucky? Well, do ya punk?
The plausible combinations outside the bag gives you the odds. picking blindfolded from the tree odds are 50/50.
From bag A the odds are 66%, bag B 62.5% were there bag C with 1 known and 4 unknown 60%, bag alpha with 1 known and 1 unknown 75%.
Basically no matter how you phrase the question there is a bag with 1 good apple and x-1 apples of unknown status in it the odds of picking a good apple is x+1/2x where x is the number of apples in the bag
The context of the question being posed, that of how to evaluate data that forms opinion polling, especially allocating don't knows and certain to votes, surely leads us to the answer being one of trust rather than mathematics?
That's why I plumped for B anyway, that child showed us a good apple, the other one just told us he had some
Are we sure there isn’t a conspiracy between the two children to keep their good apples?
You are not asked to choose between them until you are given information about the contents of the bags.
Armed with that information, you can calculate the odds of each bag, and select the best one.
The odds don't change during the game. They are fixed by the parameters of the game including the reveal. (In Monty Hall you choose before the reveal. Here, you don't.)
This otoh is a fixed bag of apples. It's not being reassembled after each random pick and replace. Therefore each random pick and replace does tell you something about its contents. And the more you do the more it tells you.
That's the essential difference.
But you only do it once for each bag so you don't learn any more.
The amount of information is fixed at the start of the game.
The two scenarios are different.
In one, you have information about the bag as a whole.
In the other, you have information about a specific apple.
I ran through all the possibilities in the other thread.
57% and 62.5%
Feel free to code it up and run a Monte Carlo simulation.
Yes, I hadn't seen your post but I agree 100%
That's what I just said above, you gain much more information if the one was chosen at random than if it was selected from the entire bag.
The odds of picking a good apple from either bag don't change based on the information presented.
Again, if I pick an apple from either bag and show it to you, when I put it back your odds of picking a good apple have not changed.
This is where it differs from the Monty Hall problem where 1 door is eliminated.
In this game the odds are fixed, and don't change. Both boys got lucky.
The question for you is, do you feel lucky? Well, do ya punk?
The plausible combinations outside the bag gives you the odds. picking blindfolded from the tree odds are 50/50.
From bag A the odds are 66%, bag B 62.5% were there bag C with 1 known and 4 unknown 60%, bag alpha with 1 known and 1 unknown 75%.
Basically no matter how you phrase the question there is a bag with 1 good apple and x-1 apples of unknown status in it the odds of picking a good apple is x+1/2x where x is the number of apples in the bag
The context of the question being posed, that of how to evaluate data that forms opinion polling, especially allocating don't knows and certain to votes, surely leads us to the answer being one of trust rather than mathematics?
That's why I plumped for B anyway, that child showed us a good apple, the other one just told us he had some
Are we sure there isn’t a conspiracy between the two children to keep their good apples?
If children are involved i suspect theyve been up to no good. Scrumping no doubt
You are not asked to choose between them until you are given information about the contents of the bags.
Armed with that information, you can calculate the odds of each bag, and select the best one.
The odds don't change during the game. They are fixed by the parameters of the game including the reveal. (In Monty Hall you choose before the reveal. Here, you don't.)
So now you've accepted the reveal does change the odds. Before you said it didn't.
You are not asked to choose between them until you are given information about the contents of the bags.
Armed with that information, you can calculate the odds of each bag, and select the best one.
The odds don't change during the game. They are fixed by the parameters of the game including the reveal. (In Monty Hall you choose before the reveal. Here, you don't.)
You are I think, assuming that the bags are totally random. But they are not - the information from the kids says that they are not. We have ruled out BBB and BBBB. Thus is crucial information.
Lets see if our pathetic Prime Minister can raise is game tomorrow from pathetic to luke warm and show this sort of spirit. Otherwise the party will boot him out.
You are not asked to choose between them until you are given information about the contents of the bags.
Armed with that information, you can calculate the odds of each bag, and select the best one.
The odds don't change during the game. They are fixed by the parameters of the game including the reveal. (In Monty Hall you choose before the reveal. Here, you don't.)
You are I think, assuming that the bags are totally random. But they are not - the information from the kids says that they are not. We have ruled out BBB and BBBB. Thus is crucial information.
Information that is available to you at the start of the game, before you calculate the odds. It doesn't change the odds during the game.
You are not asked to choose between them until you are given information about the contents of the bags.
Armed with that information, you can calculate the odds of each bag, and select the best one.
The odds don't change during the game. They are fixed by the parameters of the game including the reveal. (In Monty Hall you choose before the reveal. Here, you don't.)
What is the Reform predicted vote if
a) I pick 10 people in Bond Street at random and find 3 intend to vote Reform b) I tell you there are 3 Reform voters somewhere in London
You are not asked to choose between them until you are given information about the contents of the bags.
Armed with that information, you can calculate the odds of each bag, and select the best one.
The odds don't change during the game. They are fixed by the parameters of the game including the reveal. (In Monty Hall you choose before the reveal. Here, you don't.)
Let's take this to its logical extreme.
You have a series of coins that have been tossed randomly, so are either heads or tails facing up. They are hidden from view.
One pile has 100 coins. Person A views all 100 and tells you at least 1 is heads. That reveals very little information - only 1 possible outcome (100 tails) has been ruled out. If you choose one at random your chance of picking tails is essentially 50:50.
The second pile has 2 coins. You pick one at random and it is heads. You put it back in. In this scenario, you know 1 coin is heads with 100% certainty, while the second coin is 50:50. So if you pick from the pile at random you have a 75% chance of choosing heads.
You should therefore choose the second pile if you want heads.
I see some of you are still on my Apple Problem Is nearly everyone now agreed that I should take one of child B's apples? I will be posting one every week of the mods permit it. Thanks for the help.
Very interesting. Attacking a sovereign country other than in self defence is illegal in international law. As Rory says if they had had the peace talks in London would the Israelis have attackedLondon. Well worth listening to. Netanyahu has completely lost his mind.
Wrong.
If a third party country is harbouring forces/elements that are hostile to a given country, they are legitimate targets.
The precedents go back to before Napoleonic wars.
Essentially - if you are at war with country x, being present in a neutral country doesn’t protect you. You are still a legitimate target of war.
My son brought a waif home after school today, another boy in his year. I let the boy's mother he was here, then offered him a simple dinner of chicken and rice.
He is twelve.
It was the first time he had ever had rice.
I was flabbergasted.
I was 18 before I had rice
When I was a kid, every week my mum would cook some concoction with lentils in it.
As a result, I *never* cook with lentils...
As for rice: it is simple to cook, but easy to muck up. We do it the Turkish way: fry some orzo in butter before adding the rice and water.
I like lentils tbf, and split peas. Nice bit of pease pudding. Mum was an extremely traditional English cook - and a little of thrift dishes as we weren't ever so well off. Leftover meals, bubble and squeak etc etc and plenty Yorkshires to fill you up with roasts. Suet pudding of savory and sweet kinds, proper Norfolk dumplings and simple sinkers too. Yum. But baking was where my mums family all excelled and excel, my great grandma was in service to the local big families (Gurneys etc), a senior member of various kitchens and through her the female members of my clan all bake like its second nature. As do I now tbf
You’re making me nostalgic. My maternal grandmother was in service at Blickling Hall. She was sent there after her mother, stepfather and sister all died in the last outbreak of Bubonic Plague in England. Near Ipswich in 1910.
Now bringing to mind this photo I took from an old WW2 era (now deserted) hospital :
This otoh is a fixed bag of apples. It's not being reassembled after each random pick and replace. Therefore each random pick and replace does tell you something about its contents. And the more you do the more it tells you.
That's the essential difference.
But you only do it once for each bag so you don't learn any more.
The amount of information is fixed at the start of the game.
The two scenarios are different.
In one, you have information about the bag as a whole.
In the other, you have information about a specific apple.
I ran through all the possibilities in the other thread.
57% and 62.5%
Feel free to code it up and run a Monte Carlo simulation.
Yes, I hadn't seen your post but I agree 100%
That's what I just said above, you gain much more information if the one was chosen at random than if it was selected from the entire bag.
I had thought of doing a Monte Carlo @Flatlander. That's what I did with the Monty Hall problem. The problem though is I don't think we all agree what the coding would be! We all agree, I think, that your chances of getting a good apple from Child B are 62.5%. But we don't agree about the maths for Child A.
I still don't think there are seven equally likely scenarios.
I think you are choosing one of three apples: in one case it's definitely good, in the other two cases you have a 50/50 chance. Which gives you a 66.7% chance.
This otoh is a fixed bag of apples. It's not being reassembled after each random pick and replace. Therefore each random pick and replace does tell you something about its contents. And the more you do the more it tells you.
That's the essential difference.
But you only do it once for each bag so you don't learn any more.
The amount of information is fixed at the start of the game.
The two scenarios are different.
In one, you have information about the bag as a whole.
In the other, you have information about a specific apple.
I ran through all the possibilities in the other thread.
57% and 62.5%
Feel free to code it up and run a Monte Carlo simulation.
Yes, I hadn't seen your post but I agree 100%
That's what I just said above, you gain much more information if the one was chosen at random than if it was selected from the entire bag.
But you lose it as soon as the apple is returned to the bag and essentially rerandomised.
If this evening proves anything, it's that a week isn't just a long time in politics, it's an eternity in football.
A propos very little, a chance conversation with our local Vicar this afternoon led me to discovering Kimbanguism - nothing to do with North Korea but the Congo.
It turned out and this may be no surprise given the ethnic diversity of East Ham, said Vicar had been due to meet a Malayalam Church group - Malayalam is, as we know, the main language of the Kerala people who do fantastic things with fish.
Anyway, said Vicar got the time wrong and when she reached the Church hall she was confronted by a group of immaculately dressed (including military uniform) Congolese who were adherents of the Church of KImbangu named after one Simon Kimbangu.
There are apparently anywhere up to 2 million Congolese exiled from their country living in western Europe and North America. About 11,000 live in London mainly in north and east London with 3,000 in Barking & Dagenham.
You are not asked to choose between them until you are given information about the contents of the bags.
Armed with that information, you can calculate the odds of each bag, and select the best one.
The odds don't change during the game. They are fixed by the parameters of the game including the reveal. (In Monty Hall you choose before the reveal. Here, you don't.)
You are I think, assuming that the bags are totally random. But they are not - the information from the kids says that they are not. We have ruled out BBB and BBBB. Thus is crucial information.
If bag A the good apple is chosen from any good apples, while bag B the good apple is chosen at random, then we've eliminated many more outcomes from B.
In bag A we have eliminated BBB
In bag B we have eliminated BBBB, BBBG, BBGB, BBGG, BGBB, BGBG, BGGB, BGGG
Very interesting. Attacking a sovereign country other than in self defence is illegal in international law. As Rory says if they had had the peace talks in London would the Israelis have attackedLondon. Well worth listening to. Netanyahu has completely lost his mind.
Wrong.
If a third party country is harbouring forces/elements that are hostile to a given country, they are legitimate targets.
The precedents go back to before Napoleonic wars.
Essentially - if you are at war with country x, being present in a neutral country doesn’t protect you. You are still a legitimate target of war.
Apparently 5 members of Hamas were killed in the strike
Why would you tie your money up for years to get a 1% rate of return ?
It's only worth doing really if you have laid other runners. I laid Rupert Lowe at 23, thought it should be 1000, but really it wasn't worth the small amount U would win, so I have ended up making a book laying loads of others too.
But whether you do it or not, it's still interesting betting info. Someone thinks there is a greater than 1% of him being next PM. Seems mad to me
This otoh is a fixed bag of apples. It's not being reassembled after each random pick and replace. Therefore each random pick and replace does tell you something about its contents. And the more you do the more it tells you.
That's the essential difference.
But you only do it once for each bag so you don't learn any more.
The amount of information is fixed at the start of the game.
The two scenarios are different.
In one, you have information about the bag as a whole.
In the other, you have information about a specific apple.
I ran through all the possibilities in the other thread.
57% and 62.5%
Feel free to code it up and run a Monte Carlo simulation.
Yes, I hadn't seen your post but I agree 100%
That's what I just said above, you gain much more information if the one was chosen at random than if it was selected from the entire bag.
I had thought of doing a Monte Carlo @Flatlander. That's what I did with the Monty Hall problem. The problem though is I don't think we all agree what the coding would be! We all agree, I think, that your chances of getting a good apple from Child B are 62.5%. But we don't agree about the maths for Child A.
I still don't think there are seven equally likely scenarios.
I think you are choosing one of three apples: in one case it's definitely good, in the other two cases you have a 50/50 chance. Which gives you a 66.7% chance.
I am thinking of it thus:
Pick 3 apples randomly.
Allow a random choice from the 3 only if one or more is good.
Very interesting. Attacking a sovereign country other than in self defence is illegal in international law. As Rory says if they had had the peace talks in London would the Israelis have attackedLondon. Well worth listening to. Netanyahu has completely lost his mind.
Wrong.
If a third party country is harbouring forces/elements that are hostile to a given country, they are legitimate targets.
The precedents go back to before Napoleonic wars.
Essentially - if you are at war with country x, being present in a neutral country doesn’t protect you. You are still a legitimate target of war.
Apparently 5 members of Hamas were killed in the strike
Well done Israel.
No surprise to see roger complaining about Hamas leadership being attacked and falsely claiming international law.
Hamas are legitimate targets. Hitting them, anywhere, is legitimate.
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?
Let's number the apples physically, so child A has apples numbered 1-3, child B has apples numbered 1-4.
We will designated G as good, B as bad
Child A says, at least one of mine has no holes.
This rules in (at equal probability): ggg, ggb, GBG, bgg, gbb, bgb, bbg
and rules out: Bbb
Shifts the probability of picking a good apple from 12/24 to 12/21 by removing the 3 bads option = 57.1%
We have not used the numbers.
Child B removes 1 apple from the bag, at random, and finds it is good. For the sake of argument we'll say apple 1 has been removed, though it works exactly the same if apples 2 or 3 or 4 are found to be good.
This rules in (at equal probability): Gggg, gggb, ggbg, gbgg, ggbb, gbgb, gbbg, gbbb
(Notice how much more has been ruled out by saying apple #1 of the 4 is good rather than one of the three apples is good)
Shifts the probability of picking a good apple from 32/64 to 20/32 by removing all the bad apple #1 options) = 62.5%
Another go.
So, we have agreement for Child B, I think, that when you randomly select the first apple and find it good, that doesn't change the 50/50 chance on the other apples.
What is in dispute is whether Child A is the same case. So, I'm going to do some prestidigitation with Child A.
STEP 1: He has 3 apples in a bag. The standard 50/50 probability distribution is:
1/8 chance of no good apples 3/8 chance of one good apple 3/8 chance of two good apples 1/8 chance of three good apples
STEP 2: Let's ask him to look and see if there is a good apple in the bag. This is no different from him proferring the information. He says yes.
This leaves us: 3/7 chance of 1 good apple 3/7 chance of 2 good apples 1/7 chance of 3 good apples
Note, we've created an asymmetry and there are slightly more good apples than bad apples.
STEP 3: At this stage Scott et al note that the stated good apple has 100% chance of being good and mentally set it aside.
So, we are going to ask the boy to do the same: look, take one good apple out of the bag and physically set it aside.
This leaves us, in the bag: 3/7 chance of there being no good apples 3/7 chance of there being one good apple 1/7 chance of there being two good apples
Here, Scott claims there is a 50/50 chance of each of the remaining two apples being good. But he has selectively removed one good apple in his head, so it has biased the bag back towards bad apples in a way that Child B's random good apple did not.
The actual chance of picking a good apple from the last two on each dip is only 5/14 or 35.7%, not 50%.
Mon the Icemen! Well done to Cape verde for beating Cameroon, now one win away from WC 2026
I assume Onana was in goal for Cameroon
Indeed, he is getting some criticism for it, perhaps unfairly. Was a brilliant shot by the Cape verde forward, left 3 defenders trailing him before rifling a shot home
This otoh is a fixed bag of apples. It's not being reassembled after each random pick and replace. Therefore each random pick and replace does tell you something about its contents. And the more you do the more it tells you.
That's the essential difference.
But you only do it once for each bag so you don't learn any more.
The amount of information is fixed at the start of the game.
The two scenarios are different.
In one, you have information about the bag as a whole.
In the other, you have information about a specific apple.
I ran through all the possibilities in the other thread.
57% and 62.5%
Feel free to code it up and run a Monte Carlo simulation.
Yes, I hadn't seen your post but I agree 100%
That's what I just said above, you gain much more information if the one was chosen at random than if it was selected from the entire bag.
But you lose it as soon as the apple is returned to the bag and essentially rerandomised.
No, you don't.
If bag A chose the good one from any available good ones then that means the only information you've gained is they're not all bad. That combination is eliminated, but all other ones remain. It could be the only good one and it will still be shown.
If bag B chose the good one at random that means that good one is locked in at 100%, while others remain locked in at 50%. Much more information gained. It could be the only bad one, but was still shown, unlike the other scenario.
Mon the Icemen! Well done to Cape verde for beating Cameroon, now one win away from WC 2026
I assume Onana was in goal for Cameroon
Indeed, he is getting some criticism for it, perhaps unfairly. Was a brilliant shot by the Cape verde forward, left 3 defenders trailing him before rifling a shot home
To be fair I think Cape verde would beat Grimsby
Looks like he is leaving Man Utd to the supporters huge sigh of relief
I very much regret that I don't have the spare brain power at the moment to dedicate to the apple conundrum, or frankly even read the apple conundrum.
That's a great shame. What the thread could really use if you crunching it and coming up with an answer that's radically different to everybody else's.
Expect him to last for all of 5 minutes, he is another centre right PM proposing spending cuts in a parliament where the left have most seats and want to tax the rich instead.
Macron is just naive thinking a non centre left PM can get anything through
Isn't the null hypothesis that the apples all came from the same tree, and the children involved are equally completely untrained at apple-picking, so it doesn't matter which bag you pick from?
And if you don't want tears before bedtime, you should take one apple from each, to show that you don't have favourites?
STEP 3: At this stage Scott et al note that the stated good apple has 100% chance of being good and mentally set it aside.
So, we are going to ask the boy to do the same: look, take one good apple out of the bag and physically set it aside.
This leaves us, in the bag: 3/7 chance of there being no good apples 3/7 chance of there being one good apple 1/7 chance of there being two good apples
Here, Scott claims there is a 50/50 chance of the remaining two apples being good. But he has selectively removed one good apple in his head, so it has biased the bag back towards bad apples in a way that Child B's random good apple did not.
The actual chance of picking a good apple from the last two on each dip is only 5/14 or 35.7%, not 50%.
But this is not what happens. We don't remove the good one. We pick one at random from the bag. The odds are as stated
3/7 chance of 1 good apple 3/7 chance of 2 good apples 1/7 chance of 3 good apples
Given those odds, what are the chances that the random apple you pick out of the bag is good?
Comments
I don't actually see what this affectionate birthday greeting tells us about Mandelson that we didn't know. He was always a poor choice of ambassador.
Thank you for your attention to this matter.
One of the paradoxes of extremely harsh sentences is that juries become reluctant to convict.
But if its locked into being a six, as it won't be re-rolled, then yes of course it changes the odds. If I say bag A has 3 dice, one of which I can see is showing a 6 then of course the odds change over not knowing beforehand.
The set of possible outcomes has changed as soon as you acquired new information.
A good apple is locked into being a good apple, it won't magically become bad or spoil.
They way overestimated the actual price, so BA doubled the price of scheduled LHR<>JFK Concorde tickets.
A tiny percentage had actually booked it themselves, most being booked by PAs and on behalf of others via agents and management companies.
I don’t know why Twitter is spamming the piss diamonds twitter feed into my timeline.
https://x.com/libdems/status/1965475860867129793?s=61
The odds in the bag are fixed. They don't change no matter how often you pick right. Any right pick doesn't change the odds of the next pick.
But you don't have 1000 picks
There are 2 bags. The odds in each bag are fixed. Which bag do you pick?
(The TLDR is something like- if the costs to date are written off, it only has to fly a couple of hours a day, unlike an easyJet Airbus now. Then you can fly full with a small number of people paying top whack for decent cheese and wine. And then the costs work. There's a brilliant telling of the tale in Francis Spufford's book, Backroom Boys.)
Let's try this
1 bag with 1 apple. You know 1 apple is good. What are your odds of picking a good apple from that bag?
1 bag with 2 apples. You know 1 apple is good. What are your odds of picking a good apple from that bag?
1 bag with 3 apples. You know 1 apple is good. What are your odds of picking a good apple from that bag?
1 bag with 4 apples. You know 1 apple is good. What are your odds of picking a good apple from that bag?
The original question is about comparative odds between the bags. The odds don't change during the game.
Knowing 1 apple is good changes the comparative odds between the bags at the start of the game, but doesn't change the odds for any given bag during the game.
Epstein survivors stand with Massie, Khanna to push for Epstein Files Transparency Act
https://x.com/NewsHour/status/1963248517478306161
Every House Rules Republican just voted to block the Epstein Files Transparency Act from advancing.
https://x.com/ProjectLincoln/status/1965434232676995327
Let's take a coin, it could be heads or tails. I show a heads, next time it could be tails.
On the other hand if I take a coin out of the bag and show you both sides of the coin are heads, it's a double-headed trick coin, does that change the odds? Of course it does!
The apple is the same. Before the reveal it was a normal coin, could be heads, could be tails, could be good, could be bad, no way of knowing so it was 50%
After the reveal you know. So its no longer 50%, if you get the apple it is 100% definitely going to be good, its state can't change.
And on that if you can't be persuaded, I'm back to knitting and watching a 0-0 draw...
Before you show: 50% (50+50+50+50/4)
After you show: 62.5% (100+50+50+50/4)
The UK's elections watchdog says it's taken three years and at least a quarter of a million pounds to fully recover from a hack that saw the private details of 40m voters accessed by Chinese cyber spies.
https://www.bbc.co.uk/news/articles/c80gl8yvj9go
But you don't know what it is, only that each apple had a 50/50 chance of being one thing or the other.
By picking one out, and finding it's a good one, you have changed your knowledge. Every other apple still has a 50/50 chance of being either good or bad.
You don't understand the Monty Hall problem.
This otoh is a fixed bag of apples. It's not being reassembled after each random pick and replace. Therefore each random pick and replace does tell you something about its contents. And the more you do the more it tells you.
That's the essential difference.
The fact that a good one is pulled out of one the bags at random gives us a bit of information about the content of that bag. It makes a distribution of three good apples/one bad apple slightly more likely than one good apple/three bad apples, whereas before you pulled the good apple out those distributions would have been equally likely.
https://www.youtube.com/watch?v=XzYLHOX50Bc
Yes it’s a totally genuine film, doesn’t cut away and the coin is a real coin.
If the person doing the reveal can choose the white one (as long as any are present) that greatly reduces the information you've gained.
If they can select any white, if any exist, then you are only eliminating the 4 blacks outcome. If the 1st one is black they pick the 2nd and show it if its white, if that's black they show the third if its white, etc
If a random one has been chosen and it happened to be black, you're eliminating all the possible outcomes for that ball. They're showing you the 1st one so you know more now.
We can calculate the odds for each bag, and pick the best one.
The ‘lanyard class’ of Brussels
It’s a sign of the times that something once used to keep knives secure now carries an official name card
Alice Hancock" (£)
https://www.ft.com/content/0d4429c2-7a7b-4558-8a65-07d1df9c296b
Isn't that something that's a certainty; e.g. that your ship will sink?
(Yes, I am going to sail straight to Hull...)
The amount of information is fixed at the start of the game.
Since the set of possible outcomes is the denominator for any probability question, changing the denominator changes the probability.
Prior to the reveal, the bag could have had all bad apples, after the reveal it can't. Different set of possible outcomes, therefore different odds.
Which is why it’s a very political case, it illustrates just how crazy some of the cities in the US have got when it comes to crime. The mayor of Charlotte made a very generic statement about mental health and homelessness, without any reference to the victim of the murder. https://x.com/libsoftiktok/status/1964739505912762785
Without wishing to go all @Leon, this case is a potential breaking point in race relations in the US.
https://www.bbc.co.uk/sport/football/live/c9qngqxznn5t
That's why I plumped for B anyway, that child showed us a good apple, the other one just told us he had some
In one, you have information about the bag as a whole.
In the other, you have information about a specific apple.
I ran through all the possibilities in the other thread.
57% and 62.5%
Feel free to code it up and run a Monte Carlo simulation.
https://www.youtube.com/shorts/9pB14c9c6t8
There are 2 bags
You are not asked to choose between them until you are given information about the contents of the bags.
Armed with that information, you can calculate the odds of each bag, and select the best one.
The odds don't change during the game. They are fixed by the parameters of the game including the reveal. (In Monty Hall you choose before the reveal. Here, you don't.)
That's what I just said above, you gain much more information if the one was chosen at random than if it was selected from the entire bag.
https://www.youtube.com/shorts/DK0gbKlsG58
OK, I give up
a) I pick 10 people in Bond Street at random and find 3 intend to vote Reform
b) I tell you there are 3 Reform voters somewhere in London
You have a series of coins that have been tossed randomly, so are either heads or tails facing up. They are hidden from view.
One pile has 100 coins. Person A views all 100 and tells you at least 1 is heads. That reveals very little information - only 1 possible outcome (100 tails) has been ruled out. If you choose one at random your chance of picking tails is essentially 50:50.
The second pile has 2 coins. You pick one at random and it is heads. You put it back in. In this scenario, you know 1 coin is heads with 100% certainty, while the second coin is 50:50. So if you pick from the pile at random you have a 75% chance of choosing heads.
You should therefore choose the second pile if you want heads.
If a third party country is harbouring forces/elements that are hostile to a given country, they are legitimate targets.
The precedents go back to before Napoleonic wars.
Essentially - if you are at war with country x, being present in a neutral country doesn’t protect you. You are still a legitimate target of war.
https://prometheusjournal.org/2025/09/09/whose-party-is-it-anyway/
BBC News - Mandelson called Epstein 'best pal' in birthday message
https://www.bbc.com/news/articles/cwy9dwe50leo
We all agree, I think, that your chances of getting a good apple from Child B are 62.5%.
But we don't agree about the maths for Child A.
I still don't think there are seven equally likely scenarios.
I think you are choosing one of three apples: in one case it's definitely good, in the other two cases you have a 50/50 chance. Which gives you a 66.7% chance.
If this evening proves anything, it's that a week isn't just a long time in politics, it's an eternity in football.
A propos very little, a chance conversation with our local Vicar this afternoon led me to discovering Kimbanguism - nothing to do with North Korea but the Congo.
It turned out and this may be no surprise given the ethnic diversity of East Ham, said Vicar had been due to meet a Malayalam Church group - Malayalam is, as we know, the main language of the Kerala people who do fantastic things with fish.
Anyway, said Vicar got the time wrong and when she reached the Church hall she was confronted by a group of immaculately dressed (including military uniform) Congolese who were adherents of the Church of KImbangu named after one Simon Kimbangu.
There are apparently anywhere up to 2 million Congolese exiled from their country living in western Europe and North America. About 11,000 live in London mainly in north and east London with 3,000 in Barking & Dagenham.
In bag A we have eliminated BBB
In bag B we have eliminated BBBB, BBBG, BBGB, BBGG, BGBB, BGBG, BGGB, BGGG
So choose bag B.
But whether you do it or not, it's still interesting betting info. Someone thinks there is a greater than 1% of him being next PM. Seems mad to me
Pick 3 apples randomly.
Allow a random choice from the 3 only if one or more is good.
Otherwise pick the 3 again.
The sneaky devils. They'll never out-do Liz.
No surprise to see roger complaining about Hamas leadership being attacked and falsely claiming international law.
Hamas are legitimate targets. Hitting them, anywhere, is legitimate.
Indeed Macron may yet have to call a presidential election
So, we have agreement for Child B, I think, that when you randomly select the first apple and find it good, that doesn't change the 50/50 chance on the other apples.
What is in dispute is whether Child A is the same case. So, I'm going to do some prestidigitation with Child A.
STEP 1:
He has 3 apples in a bag. The standard 50/50 probability distribution is:
1/8 chance of no good apples
3/8 chance of one good apple
3/8 chance of two good apples
1/8 chance of three good apples
STEP 2:
Let's ask him to look and see if there is a good apple in the bag. This is no different from him proferring the information. He says yes.
This leaves us:
3/7 chance of 1 good apple
3/7 chance of 2 good apples
1/7 chance of 3 good apples
Note, we've created an asymmetry and there are slightly more good apples than bad apples.
STEP 3:
At this stage Scott et al note that the stated good apple has 100% chance of being good and mentally set it aside.
So, we are going to ask the boy to do the same: look, take one good apple out of the bag and physically set it aside.
This leaves us, in the bag:
3/7 chance of there being no good apples
3/7 chance of there being one good apple
1/7 chance of there being two good apples
Here, Scott claims there is a 50/50 chance of each of the remaining two apples being good. But he has selectively removed one good apple in his head, so it has biased the bag back towards bad apples in a way that Child B's random good apple did not.
The actual chance of picking a good apple from the last two on each dip is only 5/14 or 35.7%, not 50%.
To be fair I think Cape verde would beat Grimsby
If bag A chose the good one from any available good ones then that means the only information you've gained is they're not all bad. That combination is eliminated, but all other ones remain. It could be the only good one and it will still be shown.
If bag B chose the good one at random that means that good one is locked in at 100%, while others remain locked in at 50%. Much more information gained. It could be the only bad one, but was still shown, unlike the other scenario.
Macron is just naive thinking a non centre left PM can get anything through
And if you don't want tears before bedtime, you should take one apple from each, to show that you don't have favourites?
3/7 chance of 1 good apple
3/7 chance of 2 good apples
1/7 chance of 3 good apples
Given those odds, what are the chances that the random apple you pick out of the bag is good?