Hofzinser
12-07-2005, 03:18 PM
I'm sure most of you are familiar with the Monty Hall problem (http://en.wikipedia.org/wiki/Monty_Hall_problem).
Some friends have been arguing over a subtle variation on this which is as follows: suppose Monty picks one of the other two boxes purely at random, and just happens to pick one with a goat behind it.
Does this affect whether or not you should switch? One of my friends thinks you should still switch as you chances remain 2/3 if you do so. Another friend thinks that it now makes no difference whether you switch or not - the fact that Monty's choice was random means that there is now a 50-50 chance that your original choice was correct.
I think the second friend is correct but I'm not sure how to prove it. Can anyone provide a definitive correct answer and, ideally, a proof?
Some friends have been arguing over a subtle variation on this which is as follows: suppose Monty picks one of the other two boxes purely at random, and just happens to pick one with a goat behind it.
Does this affect whether or not you should switch? One of my friends thinks you should still switch as you chances remain 2/3 if you do so. Another friend thinks that it now makes no difference whether you switch or not - the fact that Monty's choice was random means that there is now a 50-50 chance that your original choice was correct.
I think the second friend is correct but I'm not sure how to prove it. Can anyone provide a definitive correct answer and, ideally, a proof?