Two rolls of a fair die. Let x and y be the results of the tworolls, and let z = x + y.
(a) Find P[x = 4, y = 3], P[x > 3, y = 5].
(b) Find P[z = 7], P[z = 5], P[z = 3].
(c) Find the probability that at least one 6 appears given thatz = 8.
(d) Find the probability that x = 6 given that z > 8.
(e) Find the probability that z = 7 given that at least one 4was rolled. (f) Find the probability that z > 7 given that y =4.
