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15.3 Exercise 31

Avg difficulty 2.5

Twelve solid-state modules are installed in a control system. If the modules are not defective, they have practically unlimited life. However, with probability p=0.05p = 0 . 05 any unit could have a defect which results in a lifetime (in hours) exponential (0.0025). Under the usual independence assumptions, what is the probability the unit does not fail because of a defective module in the first 500 hours after installation?

Pfeiffer, Applied Probability, 15.3 Problems on Random Selection, exercise 31

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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.