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30 January, 09:11

A study conducted at a certain college shows that 57% of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that among 9 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating.

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  1. 30 January, 09:29
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    Binomial distribution with p = 0.57, q = 1 - p = 1 - 0.57 = 0.43, n = 9

    P (X > x) = nCx * p^x * q^ (n - x)

    P (X ≥ 1) = 1 - P (0)

    P (0) = 9C0 * (0.57) ^0 * (0.43) ^9 = 1 * 1 * 0.0005026

    Therefore, the probability that at least one finds a job in his or her chosen field within a year of graduating is 1 - 0.0005026 = 0.9995 or 99.95%
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