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# Probability: jailer's reasoning

40. 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 because he already knows that at least one of the two will go free. The jailer refuses to answer this question, pointing out that if A knew which of his fellow prisoners were to be set free, then his own probability of being executed would rise from 1/3 to ½ because he would then be one of two prisoners. What do you think of the jailer's reasoning?

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#### Solution Preview

Jailer's reasoning is not correct

Probability of A being executed= 1/3
Probability of B being executed= 1/3
Probability of C being executed= 1/3

Case 1
Probability of A being executed and guard telling that B will be set free = 1/3 x ½ = 1/6
( ½ because both B and C will be set free and the guard telling that B is to be set free is ½ as he can also say that C will be set free)
Case 2
Probability of A being executed and guard telling that C will be set free = 1/3 x ½ = 1/6
( ½ because both B and C will be set free and the guard telling that C is to be set free is ½ as he ...

#### Solution Summary

Analyzes a probability question.

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