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Intro to Probability Problem

  1. Oct 25, 2007 #1
    1. The problem statement, all variables and given/known data

    The probability for a boy to be born is 51.3%.
    The probability for a girl to be born is 48.7%.
    The probabilities are independent of the sex of any children previously born to a family.
    A couple has four children.
    (a) What is the probability that all four children are girls?
    (b) What is the probability that 3 children are boys and 1 child is a girl?

    2. Relevant equations

    The product rule for probability (?)

    3. The attempt at a solution

    (a) I am thinking that if it were equally likely that a boy or a girl was to be born, then the probability that all four children being girls would be 1/16 = 0.0625 = 6.25%.

    However, with the probability of a single girl being born being 48.7%, I am wondering if I could use the product rule to say that the probability that all four children are girls is: 48.7% x 48.7% x 48.7% x 48.7% = 0.0562 = 5.62%. Is this correct?

    (b) I am thinking that if it were equally likely that a boy or a girl was to be born, then the probability that all three children being boys and 1 child being a girl would be 4/16 = 1/4 = 0.25 = 25%.

    However, with the probability of a single girl being born being 48.7%, I haven't the slightest clue how to proceed with this problem ... Could someone please grant me some assistance?

    Thank you.
     
  2. jcsd
  3. Oct 25, 2007 #2

    rock.freak667

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    Homework Helper

    I would do that same thing for the first part but for the 2nd problem I think it would be
    P(BBBG)=51.3%x51.3%x51.3%x48.7% x 4!/3!

    Note: multiply by 4!/3! because of the order in which the children can be born in
     
  4. Oct 25, 2007 #3
    Thanks! I think that does it.
     
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