Let P(A) = 0.55, P(B) = 0.30, and P(A ? B) = 0.10
a. Calculate P(A | B). (Round your answer to 2 decimal places.)
b. Calculate P(A U B). (Round your answer to 2 decimal places.)

Solution:

P(A | B) = P(A and B)/P(B) = P(AB)/P(B)

Where

P(A | B) = Probability of occurrence of A when B has occurred

P(AB) = Probability of joint occurrence of A and B = 0.10

P(B) = Marginal Probability of event B = 0.30

P(A | B) = 0.10/0.30 = 0.33

P(A U B) = P(A) + P(B) - P(A and B) = 0.55 + 0.30 - 0.10 = 0.75

Let P(A) = 0.55, P(B) = 0.30, and P(A ? B) = 0.10. a. Calculate P(A | B). (Round your answer to 2 decimal places.), b. Calculate P(A U B). (Round your answer to 2 decimal places.)

Summary:

If P(A) = 0.55, P(B) = 0.30, and P(A ? B) = 0.10 then P(A | B) = 0.33 and P(A U B) = 0.75