Probability of at Least n, with probability P, out of N

Discussion in 'Scientific Statistics Math' started by PeterOut, Jun 7, 2008.

  1. PeterOut

    PeterOut Guest

    If I randomly select a sample, the probability of it being bad is P.
    If I randomly select N samples, what is the probability that at least
    n will be bad?

    Many thanks in advance,
    PeterOut, Jun 7, 2008
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  2. PeterOut

    Phil Holman Guest

    This is a binomial distribution
    It is going to be easier to use some numbers.
    Say P = .4
    N = 5
    n = 3

    For n = 3, p(3) = 5!/(2!*3!)*.4^3*.6^2
    For n = 4, p(4) = 5!/(1!*4!)*.4^4*.6^1
    For n = 5, p(5) = 5!/(0!*5!)*.4^5*.6^0

    The probability for at least 3 to be bad is p(3) + p(4) + p(5).

    Phil H
    Phil Holman, Jun 7, 2008
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  3. PeterOut

    Phil Holman Guest

    P(X=r) = nCr*p^r*(1-p)^(n-r)

    where (nCr) = n!/[(n-r)!*r!] ......the number of possible combinations
    of r from n.

    Phil H
    Phil Holman, Jun 7, 2008
  4. PeterOut

    Bruce Weaver Guest

    --- snip ---

    There is a good binomial distribution calculator at, and probably a tutorial that would be
    relevant too.
    Bruce Weaver, Jun 7, 2008
  5. PeterOut

    PeterOut Guest

    Works great! Thank you for your help.
    PeterOut, Jun 12, 2008
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