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math

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for n repeated independent trials, with constant probability of success p for all trials, find the probability of exactly x succes n=20,p=1/8, x=2
I know the answer but I do not know how to get to that. Answer is 0.268 should I reduce fraction?

  • Statistics - ,

    To determine probability of binomial distribution for success (x=2) use the following ...
    [n choose x] * p ^x * (1-p) ^ (n-x) where
    for the first part ...
    [n choose x] =
    n! divided by [x! * (n-x!)]
    so we have 20! / (2! * 18!)
    = 20 * 19 / 2 = 190
    the second part we have
    p ^ x = (1/8) ^ 2 = 1/64 = 0.015625
    the third part we have
    (1-p) ^ (n-x) = (7/8) ^ 18 = 0.090395
    and finally 190 * 0.015625 * 0.090395 =
    0.26836

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