If P(A) = 0.4, P(B | A) = 0.35, P(A U B) = 0.69, then P(B) =?

2 Answers

• Let’s recall some rules of probability.

  P(A n B) = P(A)P(B|A) (General Multiplication Rule)

  P(A U B) = P(A) + P(B) – P(A n B) (General Addition Rule)

  So we can first find P(A n B) first using the General Multiplication Rule.

  P(A n B) = (0.4)(0.35) = 0.14

  Then we can find P(B) using the General Addition Rule.

  0.69 = 0.4 + P(B) – 0.14

  0.69 = P(B) + 0.26

  So P(B) = 0.69 – 0.26 = 0.43. The answer is B.

• If P(A) = 0.4, P(B | A) = 0.35, P(A È B) = 0.69, then P(B) =