Recall the Prisoners problem from class. We have three prisoners (A, B, and C) on death row. The Governor
will pardon one of the prisoners, and he tells the Warden who he chose, but the warden is not allowed to
reveal who was pardoned. Lets switch things up some, Prisoner C asked the warden if he was pardoned, but
the warden only will tell him that either A or B will die. Furthermore, as with the midterm problem, it is
close election time so the Governor decided to make his decision based on the proportion of people that would
dislike his choice. Because of this, we have that A has a 1
2 probability of being pardoned, B has a 1
3 probability
of being pardoned, and C has a 1
6 probability of being pardoned. Unlike in class, C knows that the warden
likes B, and if he has a choice in who he will say will die, he will always say A will die.
De�ne events A=fA is Pardonedg, B=fB is Pardonedg, C=fC is Pardonedg, and W=fWarden says B diesg.
(a) What is the event Wc in words?
(b) Make a tree diagram showing all probabilities in the tree.
(c) [ Calculate, showing all steps, P(C/Wc).
(d) Calculate, showing all steps, P(C/W).
(e) Calculate, showing all steps, P(A/W)
1 answer
1 answer