An electronic system contains three cooling components that operate independently. The probability of each component’s failure is 0.05. The

Question

An electronic system contains three cooling components that operate independently. The probability of each component’s failure is 0.05. The system will overheat if and only if at least two components fail. Calculate the probability that the system will overheat.

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Neala 5 years 2021-08-03T14:26:23+00:00 1 Answers 126 views 0

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  1. Helga
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    2021-08-03T14:27:26+00:00
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    Answer:

    Pr= 0.00725

    Step-by-step explanation:

    Given

    p = 0.05 —- probability that each component fails

    n = 3

    Required

    P(System\ Overheats)

    We understand that the system will overheat if at least 2 component fails; Assume the components are: x, y and z

    The events that the system will overheat are: xyz’, xy’z, x’yz and xyz

    Where ‘ means that the component did not fail, and the probability is 1 – p (i.e. complement rule)

    So, we have:

    xyz' \to 0.05 * 0.05 * (1 - 0.05) = 0.002375

    xy'z \to 0.05 * (1 - 0.05)* 0.05 = 0.002375

    x'yz \to (1 - 0.05)* 0.05 * 0.05 = 0.002375

    xyz \to 0.05 * 0.05 * 0.05 =0.000125

    So, the required probability is:

    Pr= 0.002375 +0.002375 +0.002375 + 0.000125

    Pr= 0.00725

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