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Math Help - child probability

  1. #1
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    child probability

    A family decides to have 20 children. Find the probability of:

    a) no girls
    b)exactly 19 boys
    c)at least 1 girl
    d) at most 1 boy

    please help and show your work or atleast explain how i can arrive at the answer
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  2. #2
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    Quote Originally Posted by drewbear View Post
    A family decides to have 20 children. Find the probability of:

    a) no girls
    b)exactly 19 boys
    c)at least 1 girl
    d) at most 1 boy

    please help and show your work or atleast explain how i can arrive at the answer
    Lets assume X~Binomial(n=no of trials, p= probability of success)

    The binomial theorem states P(X=k) = \binom{n}{k}p^k(1-p)^{n-k}

    In your case lets call X the probability of having a girl with n= 20 and p = 0.5

    a) find P(X=0)

    b) exactly 19 boys = exactly 1 girl so find P(X=1)

    c) "at least 1" means 1 or more so find P(X\geq 1) = P(X=1)+P(X=2)+\dots+P(X=20)

    Remember P(A) = 1 - P(A')

    d) "at most 1" means 1 or less so this means 2 or more girls now find P(X\geq 2) = P(X=2)+P(X=3)+\dots+P(X=20)
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