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Back to 4.4 Problems on Independence of Events

4.4 Exercise 15

Avg difficulty 2.5

Consider the pair {A,B}\left\{A , B\right\} of events. Let P(A)=pP \left(A\right) = p, P(Ac)=q=1-pP \left(A^{c}\right) = q = 1 - p, P(B|A)=p1P \left(\right. B \left|\right. A \left.\right) = p_{1}, and P(B|Ac)=p2P \left(\right. B \left|\right. A^{c} \left.\right) = p_{2}. Under what condition is the pair {A,B}\left\{A , B\right\} independent?

Pfeiffer, Applied Probability, 4.4 Problems on Independence of Events, exercise 15

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Adapted from Applied Probability © 2009 Paul E. Pfeiffer. Licensed under CC BY 3.0. Source: Applied Probability. Imported at revision d7a0420.