1. ## probability

Given that 3 prisoners A, B, C are to be sentence to death, but each knows that one of them at random with equal probability is to be pardoned. Given that the governor tells A that B is to be executed, what is the probability that A will be pardoned.

2. Originally Posted by alexandrabel90
Given that 3 prisoners A, B, C are to be sentence to death, but each knows that one of them at random with equal probability is to be pardoned. Given that the governor tells A that B is to be executed, what is the probability that A will be pardoned.
1/3

3. may i know how to get the probability of that?

i know that i have to use conditional probability but i cant find the P( the governor tells A l A is pardon) and the P ( governor tells A l that C is pardon )...

4. This is a very common brain teaser...

Basically, the governor could be lying, so you did not gain any information.

Wikipedia "The Problem of Three Prisoners" or something like this...

5. i know that P( the governor tells A l A is pardon) should be 0.5 and the P ( governor tells A l that C is pardon ) = 1 but i dont get it after reading wiki's "three prisoners"

6. Originally Posted by alexandrabel90
i know that P( the governor tells A l A is pardon) should be 0.5 and the P ( governor tells A l that C is pardon ) = 1 but i dont get it after reading wiki's "three prisoners"
The accepted answer is 1/3, because A knows one of B and C will be executed
and knowing that it is B rather than C surely does not aid his cause.

I don't know if it's been examined in complete detail,
but consider this.....

A knows B is done for if no-one's mind can be changed regarding the decision.

C doesn't know and B doesn't know.
C may consider himself to have a 1 in 3 chance of survival.
B may consider himself to have a 1 in 3 chance of survival.

A knows B has a zero chance of survival,
while B and C do not have that data.

Under the circumstances, are C and B's calculations incorrect
given that they do not have access to all the information ?

Is the situation we are now presented with....
2 prisoners, 1 of whom is going to be set free?

This may be so if the decision of who goes free has not been made yet.

However, if there was a single decision in the beginning to decide who would be set free randomly, the probabilities are 1/3 before then.

Do the probabilities change after the decision?
It depends on the decision.
If the decision was "who goes free", then 2 are done for absolutely.
They both now have a zero chance of survival, they just don't know it.

Well, B is certainly done for!
His probability has changed.
What about A and C ?

Two scenarios are....