Question

If P(A) = 0.5, P(B) = 0.3, and P(A or B) = 0.6, find P(A and B)

Answer 1

P(A or B) = P(A) + P(B) - P(A and B), which means that the probability that A or B occurs is equal to the probability that A occurs plus the probability that B occurs minus the probability that both A and B occur.

So, you know P(A), P(B) and P(A or B) and you can solve for P A and B) =>

P(A and B) = P(A) + P(B) - P(A or B)

P(A and B) = 0.5 + 0.3 - 0.6 = 0.8 - 0.6 = 0.2

Answer: P(A and B) = 0.2