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Can someone please help me with a Statistics problem? Need help finding the probabilities?

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  • 3 years ago
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    Use the binomial probability formula:

    P(X = k) = C(n,k) * p^k * q^(n-k)

    n : number of trials (11)

    k : number of "successes" (2 bad grapefruit)

    p : probability of "success" (0.19)

    q : probability of "failure" (1-p = 0.81)

    I think you can just plug that in and get the answer you need:

    P(X = 2) = C(11,2) * 0.19^2 * 0.81^9

    As for part B, you should consider the opposite case. Figure out the probability of getting 0 bad grapefruit or 1 bad grapefruit and subtract from 1.

    P(X ≥ 2) = 1 - P(X < 2)

    = 1 - (P(X = 0) + P(X = 1))

    You have the formula for P(X = k), so just plug in k=0 and k=1, then subtract that from 1.

    P(X = 0) = C(11,0) * 0.19^0 * 0.81^11

    P(X = 1) = C(11,1) * 0.19^1 * 0.81^10

    P(X ≥ 2) = 1 - (P(X = 0) + P(X = 1))

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