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Back to 5.3 Problems on Conditional Independence

5.3 Exercise 11

Avg difficulty 2.5

A company is considering a new product now undergoing field testing. Let

  1. H be the event the product is introduced and successful
  2. S be the event the R&D group produces a product with the desired characteristics.
  3. E be the event the testing program indicates the product is satisfactory

The company assumes P(S)=0.9P \left(S\right) = 0 . 9 and the conditional probabilities

P ( H | S ) = 0 . 90 P ( H | S c ) = 0 . 10 P ( E | S ) = 0 . 95 P ( E | S c ) = 0 . 15 P \left(\right. H \left|\right. S \left.\right) = 0 . 90 P \left(\right. H \left|\right. S^{c} \left.\right) = 0 . 10 P \left(\right. E \left|\right. S \left.\right) = 0 . 95 P \left(\right. E \left|\right. S^{c} \left.\right) = 0 . 15

Since the testing of the merchandise is not affected by market success or failure, it seems reasonable to suppose {H,E} ci |S\left\{H , E\right\} ci \left|\right. S and ci |Scci \left|\right. S^{c}. The field tests are favorable. Determine P(H|E)/P(Hc|E)P \left(\right. H \left|\right. E \left.\right) / P \left(\right. H^{c} \left|\right. E \left.\right).

Pfeiffer, Applied Probability, 5.3 Problems on Conditional Independence, exercise 11

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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.