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26 July, 05:18

The process that you monitor relies on 10 cooling pumps. As long as 6 are running the process can continue. In one hour any of the pumps has a 10% chance of being clogged. What is the probability that you will have exactly 4 failures in one hour? Round off to the fourth decimal place.

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  1. 26 July, 05:39
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    The probability that you will have exactly 4 failures in one hour = 0.0112

    Step-by-step explanation:

    Number of pumps = 10

    Probability of failure for the pumps in an hour = 0.10

    Probability required is the probability that 4 out of 10 pumps fail in an hour.

    This is a binomial distribution problem

    Binomial distribution function is represented by

    P (X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

    n = total number of sample spaces = total number of pumps

    x = Number of successes required = in this case, number of failure required = 4

    p = probability of success = probability that a pump actually fails = 0.1

    q = probability of failure = probability that a pump doesn't fail = 0.9

    The wordings of the question seem to counter the definition of parameters in the formula, but it is the understanding that is key.

    P (X=4) = ¹⁰C₄ (0.1) ⁴ (0.9) ¹⁰⁻⁴ = 0.011160261 = 0.0112
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