1. (8 points total) Suppose that A, B, and C are events. For each of the following statements, circle the T if it is true and the F if it is false. If it is true, briefly explain your reasoning (2-3 sentences) in the space provided. If it is false, give an example for which the statement is false (also called a counterexample). (a) (4 points) If P(A)+P(B)+P(C) = 1, then the events A, B, and C are disjoint. T F (b) (4 points) For any two events A and B, P(AUB) = P(A)+P(B). T F Solution a) False; If Pr(A) = .5, Pr(B) = .3. Pr(C) = .2, where Pr(A?B)=.2 then Pr(A)+Pr(B)+Pr(C) will equal 1 but the events are not disjoint. The Pr(A?B?C) would be < 1. b) False; The Pr(AUB) would equal Pr(A) + Pr(B) if the events A and B are disjoint. If they are not, then the Pr(AUB) would equal Pr(A) + Pr(B) - Pr(A?B)..