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.
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....
1. The decision has already been made
2. The decision of who to set free was not made, only the first prisoner to go was decided.
Now the 2nd will be decided.
If it is scenario 2, then we can say there are 2 people with equal chance of freedom.
If it is scenario 1, what do we say ?