Question : There are three prisoners A, B and C. A knows that two of the three are going to be released. Obviously the probability that A is released is 2/3. Now A becomes curious and asks the jailor,”Which two of us will be let go?”
The jailor replies,”Well, I cannot tell you that, but B is going to be set free. That is all I can tell you.”
A gets disappointed and goes back to his cell and starts thinking about the new probability of his discharge.
Has the probability really changed? If no, why? and if yes why and what is the new value?
Answer : Sorry guys, I don’t know the solution. If you know it, post as comment here. I can update here.
Initially, these are the possibilities of candidates being released. (The candidates in brackets imply the ones that are being released)
[AB]C, [AC]B, [BC]A
Here: A has a probability of 2/3 in getting out.
When the jailer mentioned that B is certainly going to be released, the set [AC] B is ruled out.
There fore the probability of A has come down from 2/3 to 1/2.
A probability stays 2/3, its C who is f###ed up and his probability has gone down to 1/3.
Think about it. yes. I am a genius.