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Back to 3.2 Problems on Conditional Probability

3.2 Exercise 18

Avg difficulty 2.5

Use property (CP4) to show

  1. P ( A | B ) > P ( A ) iff P ( A | B c ) < P ( A ) P \left(\right. A \left|\right. B \left.\right) > P \left(A\right) \text{iff} P \left(\right. A \left|\right. B^{c} \left.\right) < P \left(A\right)
  2. P ( A c | B ) > P ( A c ) iff P ( A | B ) < P ( A ) P \left(\right. A^{c} \left|\right. B \left.\right) > P \left(A^{c}\right) \text{iff} P \left(\right. A \left|\right. B \left.\right) < P \left(A\right)
  3. P ( A | B ) > P ( A ) iff P ( A c | B c ) > P ( A c ) P \left(\right. A \left|\right. B \left.\right) > P \left(A\right) \text{iff} P \left(\right. A^{c} \left|\right. B^{c} \left.\right) > P \left(A^{c}\right)

Pfeiffer, Applied Probability, 3.2 Problems on Conditional Probability, exercise 18

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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.