>
> Here's a real humdinger: if you're on a game show where there's a prize
> behind one door and x number of booby prizes behind the other doors, you
> should always switch from your original choice (at least, if you want to
> heighten your chances of winning) after the booby prizes have been
> revealed and only two doors remain (the one you chose and the one that
> probably has the prize behind it).
>
indeed. this has been described many times over, but keith devlin has an interesting bit on probability in his book "goodbye descartes" where he outlines the "monty hall problem" above quite nicely (monty hall because of an american show that uses a similar theme).
as evident in the discussions on this list, this and other computations in probability seem to face a lot of challenge (since they run a bit counter-intuitive?). i like to add to the confusion by offering this explanation for the three door scenario: lets say you chose door1. probability that the prize is behind door1 is 1/3, probability that its not is 2/3. if door3 is opened to reveal no prize, then it follows that the probability that its behind door2 is now 1-prob(door1) = 2/3 ;-). so, you would be smart to switch your choice to door2!
--ravi
-------------------------------------------------------------------------------- man is said to be a rational animal. i do not know why he has not been defined as an affective or feeling animal. more often i have seen a cat reason than laugh or weep. perhaps it weeps or laughs inwardly - but then perhaps, also inwardly, the crab resolves equations of the 2nd degree. -- alasdair macintyre.