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27 October, 03:34

A town has two fire engines operating independently. The probability that a specific engine is available when needed is 0.96. (a) What is the probability that neither is available when needed? (b) What is the probability that a fire engine is available when needed?

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  1. 27 October, 05:28
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    Answer is

    a. P (both pumps not available) = 0.016

    b. P (both pumps available) = 0.984

    Step-by-step explanation:

    a. Probability of neither pump is available.

    We know that P1 + P2 = 1

    P1 = Probability of one pump is available = 0.96

    P2 = Probability of a pump not available = 1-0.96 = 0.04

    Now the probability of both pump not available will be = P2 x P2

    =0.04 x 0.04 = 0.016

    b. Probability of both pumps available will be.

    Using the equation of probability

    P (both pumps available) + P (both pumps unavailable) = 1

    P (both pumps available) = (1 - P (both pumps unavailable))

    P (both pumps available) = 1-0.016

    P (both pumps available) = 0.984
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