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Three prisoners are informed by their jailer that one of
Chapter 3, Problem 44P(choose chapter or problem)
Problem 44P
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 the 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 to because he would then be one of two prisoners. What do you think of the jailer’s reasoning?
Questions & Answers
QUESTION:
Problem 44P
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 the 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 to because he would then be one of two prisoners. What do you think of the jailer’s reasoning?
ANSWER:
Solution
Step 1 of 1
We have to write the jailers reasoning by using our result at the end
Let us assume that jailer told A that B is going to be freed
This turns out to be 1/3 then the jailer is wrong and it is 1/2 when the jailer is correct
Now we have to find P(A is executed / told B freed)
By using bayes rule
Now we have to find P( told B freed)
Now all the prisoners are having equal probability of being executed that is 1/3