The Environmental Protection Agency (EPA) has contracted with your company for equipment to monitor water quality for several lakes in your

Question

The Environmental Protection Agency (EPA) has contracted with your company for equipment to monitor water quality for several lakes in your water district. A total of 15 devices will be used. Assume that each device has a probability of 0.05 of failure during the course of the monitoring period. What is the probability that one of the devices fail?

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Jade 3 weeks 2021-10-08T01:08:27+00:00 1 Answer 0

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    2021-10-08T01:10:00+00:00

    Answer:

    36.58% probability that one of the devices fail

    Step-by-step explanation:

    For each device, there are only two possible outcomes. Either it fails, or it does not fail. The probability of a device failling is independent of other devices. So we use the binomial probability distribution to solve this question.

    Binomial probability distribution

    The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

    P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

    In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

    C_{n,x} = \frac{n!}{x!(n-x)!}

    And p is the probability of X happening.

    A total of 15 devices will be used.

    This means that n = 15

    Assume that each device has a probability of 0.05 of failure during the course of the monitoring period.

    This means that p = 0.05

    What is the probability that one of the devices fail?

    This is P(X = 1)

    P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

    P(X = 1) = C_{15,1}.(0.05)^{1}.(0.95)^{14} = 0.3658

    36.58% probability that one of the devices fail

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