not necessarily, how can one place odds on something that may or may not exist? Glad about the cat though, was about to inform Admin to take one or two posters to task!
Impeccable logic
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I don't actually know the answer to this, but I don't think it's fifty-fifty.
With Joe's coin, any one toss gives a 50/50 chance of heads or tails. But if you watched someone toss the coin and come up with 100 heads (or tails) then it's doubtful if you would bet on the next toss, you'd be too busy looking for the fakery, as the probability of 101 coin tosses producing the same result is negligible. So prior knowledge changes your perception of probability.
If there were two boxes and one contained £250k and the other £1 then the chance of picking the £250k would be 50/50. But this isn't the case. The other box, for want of a better name, has been chosen from 19. It could have contained £500, or £1000, or 50p, etc. Prior knowledge (i.e. how the amount in the box was determined) alters the probability.
The odds of the DonD contestant picking the £250k box from 20 is 19/1. The odds of the box being one of the others is 1/19. So the odds are very heavily on the £250 being one of the others. Now the others have been whittled down to one, is it still 19/1 that the contestant has the £250k, and 1/19 that it's in the other box?
Monty Hall gave contestants the choice of three boxes (he knew what was in which). He then opened one of the other boxes which was empty, and gave the contestant the choice of switching. The odds were determined (after much academic arguing) 1/3 that the contestant had the right box, and 2/3 that it was Monty's remaining box, so he should switch.
Now on Noel's game, if he knew what was in the boxes and opened all the others except one, the odds should be heavily on swapping. I'm not sure how opening the boxes by guessing alters things. Probably not a lot. I'd swap.
Rgds.
With Joe's coin, any one toss gives a 50/50 chance of heads or tails. But if you watched someone toss the coin and come up with 100 heads (or tails) then it's doubtful if you would bet on the next toss, you'd be too busy looking for the fakery, as the probability of 101 coin tosses producing the same result is negligible. So prior knowledge changes your perception of probability.
If there were two boxes and one contained £250k and the other £1 then the chance of picking the £250k would be 50/50. But this isn't the case. The other box, for want of a better name, has been chosen from 19. It could have contained £500, or £1000, or 50p, etc. Prior knowledge (i.e. how the amount in the box was determined) alters the probability.
The odds of the DonD contestant picking the £250k box from 20 is 19/1. The odds of the box being one of the others is 1/19. So the odds are very heavily on the £250 being one of the others. Now the others have been whittled down to one, is it still 19/1 that the contestant has the £250k, and 1/19 that it's in the other box?
Monty Hall gave contestants the choice of three boxes (he knew what was in which). He then opened one of the other boxes which was empty, and gave the contestant the choice of switching. The odds were determined (after much academic arguing) 1/3 that the contestant had the right box, and 2/3 that it was Monty's remaining box, so he should switch.
Now on Noel's game, if he knew what was in the boxes and opened all the others except one, the odds should be heavily on swapping. I'm not sure how opening the boxes by guessing alters things. Probably not a lot. I'd swap.
Rgds.
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I'm disappointed about the cat not being in the box. All domestic cats should be put in a box with poison.
I
imamartian
the probability of tossing a coin 100 times and getting a head every time is 1.267 x 10 to the power of 30 (or 1 in 1267650600228230000000000000000) however, each toss of the coin is still 50:50.
If the question was would you swap your box for the 19 boxes then of course you'd swap, there's a far higher chance that the £250k is in one of the 19 boxes. But swapping your box with one of the 19 boxes does not increase you chance of getting £250k.
And as with the 100 coins, being left with the 2 boxes that have £1 and £250k is a small probability, but once you do get to that point, then the outcome is 50:50.
If the question was would you swap your box for the 19 boxes then of course you'd swap, there's a far higher chance that the £250k is in one of the 19 boxes. But swapping your box with one of the 19 boxes does not increase you chance of getting £250k.
And as with the 100 coins, being left with the 2 boxes that have £1 and £250k is a small probability, but once you do get to that point, then the outcome is 50:50.
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What if you chose your box, and Noel knew where the £250k was, and he opened all but one of his boxes without revealing the £250k, and then offered the swap, what would you do?
That's as near as I can get to Monty H.
That's as near as I can get to Monty H.
I
imamartian
if people involved know where the £250k is then it's not probability anymore...
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Brillient
Bet he was 'Uncertain' as to the 'Principle' exercised by the policeman administering the fixed penalty notice.
oooh you'll go to hell and have to stand in 3 ft of runny cats muck during your tea break
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Tim - You haven't read 'The God Delusion' yet Eh!
There is no Hell, or Heaven for that matter, so I am OK there then!!!!!!!!!
19 times out of 20 (of the times that only two boxes are left unopened), the desired prize will be in one of the boxes that isn't the 'owned' box.Thermo said:
Therefore if you don't swap you will win that desired prize only once in 20 attempts.
Therefore if you swap you will win that desired prize 19 times in 20 attempts.
Even though I wouldn't have 20 attempts, I would play according to those odds on my single attempt.
But the single attempt scenario is a hypothetical one, because I wouldn't cope with being in the company of Noel Edmonds without punching him and being dragged off him by several heavies.
Why what? Delilah?
I
imamartian
[quote="Softus" 19 times out of 20 (of the times that only two boxes are left unopened), the desired prize will be in one of the boxes that isn't the 'owned' box.
[/quote]
but 18 of those 19 times there won't be £250k in the box
[/quote]
but 18 of those 19 times there won't be £250k in the box
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