00:01
Three prisoners are informed that one of them would be chosen at random to be executed, and the other two will be freed.
00:10
Prisoner a asks the jailer to tell him privately which of his follow two prisoners will be set free, but the jailer refuses, claiming that if he tells him, then his own probability of being executed will rise from one third to have.
00:26
We are to check if his reasoning is true.
00:30
Now, without loss of generality, let us assume that the jailer told a that b is going to be freed.
00:39
Then the probability that we are going to check will be probability of a died, given that the jailer told prisoner a that b will be freed.
00:59
Now, before we continue, then it means that if it turns out that's this probability is wanted then the jailer is wrong if it's half then the jailer is correct so let's represent probability of jailer a probability of prisoner a being told that b will be free it that represent it with w and a dead is a b dead is b dead is b and c dead is c so then this will reduce to probability of a given w.
01:47
And hence, using b's rule, this can be written as probability of w given a times probability of a all over probability of w.
02:05
Probability of w will have to be written as the joint sets...