Before, I said it\'d be 0.33 (1/3). After, I said it\'d be 0.5 (1/2). This seems

Question

Before, I said it'd be 0.33 (1/3). After, I said it'd be 0.5 (1/2). This seems too easy, though. So, I'm not sure how to do this?

(+5)*7. Three prisoners a, b and c know that exactly two of them are going to be executed, but they do not know which two. Prisoner a knows that the jailer will not tell him whether or not he is going to be executed. He therefore asks the jailer to tell him the name of one prisoner other than a himself who will be executed. The jailer responds that b will be executed. What is the probability that a will be executed before and after the answer is given to him?

Explanation / Answer

before P(a is executed) =2/3 (as two of three are supposed to be executed)

after:

P(jailor said b will be executed)=P(a and b are supposed to be executed and jailor said b)+P(b and c are supposed to be executed and jaior said b) =(1/3)*(1)+(1/3)*(1/2)=3/6 =1/2

therfore P(a will be executed|b is executed)

=P(a and b are supposed to be executed and jailor said b)/P(jailor said b)=(1/3)*(1)/(1/2)=2/3

hence after probability remains same as 2/3

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