A and B are two independent events with PA 05 and PA U B 0

A and B are two independent events with P[A] = 0.5 and P[A U B] = 0.8. What is P[B]?

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

and for independent events,

P(A n B) = P(A)P(B)

Then

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

Thus,

0.8 = 0.5 +P(B) - 0.5P(B)

0.3 = 0.5P(B)

P(B) = 0.6 [ANSWER]