Question

If A and B are events with P(A)=0.7, P(A OR B)=0.77, and P(A AND B)=0.13, find P(B).

Answer 1

P(B) = 0.20

Explanation:

For these events, which are not independent or mutually exclusive, the relation between the various probabilities is ...

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

Solving for P(B), we find ...

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

P(B) = 0.77 +0.13 -0.7 = 0.20

The probability of B is 0.20.

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Additional comment

The formula applies to independent and mutually exclusive events, as well. For independent events, P(A and B) = P(A)·P(B). For mutually exclusive events, P(A and B) = 0.