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 10 devices will be used. Assume that each device has a probability of 0.01 of failure during the course of the monitoring period. What is the probability that none of your devices fail

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Liliana 1 month 2021-09-16T15:02:19+00:00 2 Answers 0

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    0
    2021-09-16T15:03:20+00:00

    The probability that none of the devices fails happens when x = 0.

    P(none fail) = 1(0.01)^(0)•(1 – 0.01)^(10)

    P(none fail) = (0.01)^0•(0.99)^(10)

    P(none fail) = 0.90438

  1. Charlotte
    0
    2021-09-16T15:03:36+00:00

    Answer:

    Probability that none of your devices fail is 0.9044.

    Step-by-step explanation:

    We are given that 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 10 devices will be used. Assume that each device has a probability of 0.01 of failure during the course of the monitoring period.

    The above situation can be represented through Binomial distribution;

    P(X=r) = \binom{n}{r}p^{r} (1-p)^{n-r} ; x = 0,1,2,3,.....

    where, n = number of trials (samples) taken = 10 devices

                 r = number of success = none fail

                p = probability of success which is probability of failure during the

                       course of the monitoring period, i.e; 0.01.

    LET X = No. of failures

    So, it means X ~ Binom(n=10, p=0.01)

    Now, Probability that none of your devices fail is given by = P(X = 0)

          P(X = 0) =  \binom{10}{0} \times 0.01^{0} \times (1-0.01)^{10-0}

                        = 1 \times 1 \times 0.99^{10} = 0.9044

    Hence, the probability that none of your devices fail is 0.9044.

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