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Math Help - Probability

  1. #1
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    Probability

    A family has eleven children. The probability of having a girl is 1/2. What is the probability of having no more than 1 boy?

    Please show your work. Thanks in advance.
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  2. #2
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    First off I think a mod should move this since I don't think this is the right place for this topic.

    So let P(x)= probability of having x boys.
    Then you want P(0)+P(1)
    P(0) = \left(\frac{1}{2}\right)^{11} since there are no boys.
    P(1)={11\choose 1}\left(\frac{1}{2}\right)^{11} there are {11\choose 1} ways to have one boy out of a group of 11 people.
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  3. #3
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    So, if the question was like "A family has five children. The probability of having a girl is 1/2. What is the probability of having no more than 3 boys?"

    Is this how you would do that?

    <br />
P(0) = \left(\frac{1}{2}\right)^{5}<br />
    <br />
P(1) = {5\choose 1}\left(\frac{1}{2}\right)^{5}<br />
    <br />
P(2) = {5\choose 2}\left(\frac{1}{2}\right)^{5}<br />
    <br />
P(3) = {5\choose 3}\left(\frac{1}{2}\right)^{5}<br />
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  4. #4
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    Yes, that's correct.
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