1. An experiment has four possible outcomes A, B, C, and D. Check whether the following assignments of probability are possible:

(a) P(A) = 0.20,P (B) = 0.40,P(C) = 0.09,P (D) = 0.31.

(b) P(A) = 0.41,P (B) = 0.17,P(C) = 0.12,P(D) = 0.36.

(c) P(A) = 1/8,P(B) = 1/2,P(C) = 1/4,P(D) = 1/8.

2. Suppose we toss two coins and suppose that each of the four points in the sample space S = {(H, H), (H, T ), (T, H), (T, T )} is equally likely. Let the events be A = {(H, H), (H, T )} and B = {(H, H), (T, H)}. Find P(A ∪ B).