Suppose A and B are events in a sample space S and suppose that P(A) = 0.7, P(Bc) = 0.1, and P(A ∩ B) = 0.6. What is P(A ∪ B)?

Question

Suppose A and B are events in a sample space S and suppose that P(A) = 0.7, P(B^c) = 0.1, and P(A ∩ B) = 0.6. What is P(A ∪ B)?

Answer 1

Since P( B complement )=0.1 we have that P(B)=0.9 which implies that

P(A union B)=P(A)+P(B)-P(A intersection B)=0.7+0.9-0.6=1.6-0.6=1.