According to government data, the probability that an adult was never in a museum is 15%. In a random survey of 10 adults, what is the proba

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According to government data, the probability that an adult was never in a museum is 15%. In a random survey of 10 adults, what is the probability that two or fewer were never in a museum

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Isabella 2 weeks 2021-09-15T21:23:30+00:00 1 Answer 0

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    2021-09-15T21:25:19+00:00

    Answer: 0.8202

    Step-by-step explanation:

    Probability an adult was never in a museum = probability of success = p = 15% = 0.15

    To find probability that 2 or fewer of the 10 samples selected were never in a museum is given by:

    P(X=2) or P(X=1) or P(X=0).

    Where

    P(X=r) = nCr * p^r * q^n-r

    and n=10, p =0.15, q=0.85

    When r = 2

    P(X=2) = 10C2 * 0.15² * 0.85^8 = 0.2759

    When r = 1

    P(X=1) = 10C1 * 0.15 * 0.85^9 = 0.3474

    When r = 0

    P(X=0)= 10C0 * 0.15^0 * 0.85^10 = 0.1969

    Hence probability of having 2 or fewer adults who never visited the museum = 0.1969 + 0.3474+ 0.2759 = 0.8202

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