A die is rolled twice. Let Xi be the number of spots on the ith roll for i = 1, 2.

(a) Find P (X1 = 3 | X1 + X2 = 8), the conditional probability of a 3 on the first roll given a total of 8 spots.

(b) Find P (X1 + X2 = 7 | X1 = 3).

(c) Find E(X1 | X1+X2 = 6), the conditional expectation of X1 given that X1 + X2 = 6.