A,B,C are three prisoners in a jail where J is the jailor. Exactly one of the three prisoners are going to be hanged and 2 are going to be freed. J knows who will be executed but none of the prisoners do. Now prisoner A goes to J and says 'I don't want to know who will be executed but at least tell me at least one of B and C who will be freed.' But J says,'I am sorry but I can't do this because if I don't tell you who will be freed then the probability of you getting executed is 1/3, however if I tell you who will be freed among B and C, then the probability of you getting executed is 1/2. And I can't endanger you by increasing the probability of your death in this way.' However A retorts that if the jailor tells him who among B and C is going to be freed, even then the probability of A getting hanged is 1/3. Who is right - J or A?
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asked Sep 29, 2015 at 18:11
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$\begingroup$ See en.wikipedia.org/wiki/Three_Prisoners_problem $\endgroup$– Emanuele PaoliniSep 29, 2015 at 18:25
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1 Answer
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$A$, of course, is right. The probability of his being hanged is simply $1$ in $3$, and it doesn't matter whether he knows it or not.
For the jailor to say that the probability is $1$ in $2$ because there are two possible outcomes (either $A$ or $(B \textrm{ or } C)$) is like saying that the odds of winning the lottery are $1$ in $2$ because there are two outcomes, you win or you don't.
answered Sep 29, 2015 at 18:23