Michigan State University - Diagnostic Exam

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5.19

  •   A study of two fire sprinklers finds that the probability of one sprinkler going off during a fire is 90%, and the probability of the other one going off is 97%. Assuming the sprinklers work independently, what is the probability that at least one sprinkler goes off during a fire?

    a) 87.3% b) 90% c) 97% d) 99.7% e) 100%

Solution:

Let Sj denote the event “the jth sprinkler goes off”. Then

P (S1 or S2) = P(S1 ) + P (S2) - P (S1 )P (S2) = 0.90 + 0.97 - (0.90)(0.97) = 0.997

Diagnostic:

See 5.18: Probability .

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July 15, 2008