1 Let PA 0 5 PB 08 PA B 04 a Are A and B mutually exclusi

1. Let P(A) =0 .5, P(B) = 0.8, P(A ? B) = 0.4,

(a) Are A and B mutually exclusive (disjoint)? Why?

(b) Are A and B independent? Why?

(c) What is P (A U B)?

Solution

Let P(A) =0 .5, P(B) = 0.8, P(A ? B) = 0.4,

P(A U B) = P(A) + P(B) - P(A?B)

P(A U B) = 0.5 + 0.8 - 0.4

P(A U B) = P(A) + P(B) - P(A?B) = 0.9