Three prisoners are informed by their jailer that one of them has been chosen at random to be executed, and the other two are to be freed. Prisoner A asks the jailer to tell him privately which of his fellow prisoners will be set free, claiming that there would be no harm in divulging this information, since he already knows that at least one will go free. The jailer refuses to answer this question, pointing out that if A knew which of his fellows were to be set free, then his own probability of being executed would rise from to, since he would then be one of two prisoners. What do you think of the jailer's reasoning?43. Suppose we have ten coins which are such that if the ith one is flipped then heads will appear with probability i/10, 1, 2,..., 10.

When one of the coins is randomly selected and flipped, it shows heads. What is the conditional probability that it was the fifth coin?