Assume that the events A and B satisfy P(A)=P(B)=P(B/A')=1/3 where A' is complement of A. What is P(A'UB)?

Question

Assume that the events A and B satisfy

P(A)=P(B)=P(B/A')=1/3

where A' is complement of A. What is P(A'UB)?

Answer 1

P(A'UB)= P(A') + P(B) - P(A'∩B);

P(B/A') = P(A'∩B)/P(A'); P(A') = 1 - 1/3 = 2/3; P(A'∩B) = 1/3·2/3 = 2/9

P(A'UB) = 2/3 + 1/3 - 2/9 = 7/9

Answer 2

P(A')=2/3

P(A'UB)=2/3