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3.2 Exercise 20

Avg difficulty 2.5

Show that P(A|B)=P(A|BC)P(C|B)+P(A|BCc)P(Cc|B)P \left(\right. A \left|\right. B \left.\right) = P \left(\right. A \left|\right. B C \left.\right) P \left(\right. C \left|\right. B \left.\right) + P \left(\right. A \left|\right. B C^{c} \left.\right) P \left(\right. C^{c} \left|\right. B \left.\right).

Pfeiffer, Applied Probability, 3.2 Problems on Conditional Probability, exercise 20

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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.