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Another family question

  1. Sep 16, 2011 #1
    Hi
    I have some difficulties with following question.

    A family has five children. Assuming that the probability of a girl on each birth was 1/2 and that the five births were independent, what is the probability the family has at least one girl, given they have at least one boy?

    My solution is 1-(1/2)^4 = 15/16

    However according to the book correct answer it 30/31.
    Any ideas?
     
  2. jcsd
  3. Sep 18, 2011 #2

    Stephen Tashi

    User Avatar
    Science Advisor

    Look at material on the binomial distribution.

    The conditions in the problem are satisified if the family has any of the following combinations of genders:
    (exactly 1 boy and 4 girls)
    (exactly 2 boys and 3 girls)
    (exactly 3 boys and 2 girls)
    (exactly 4 boys and 1 girl)

    The conditions are not satisfied by the combinations of genders:
    (exactly 5 boys and 0 girls )
    (exactly 0 boys and 5 girls )

    The problem says we are "given" that the family has at least one boy, so you should look at the formula for conditional probability.
     
  4. Sep 20, 2011 #3
    Thanks a lot Stephen.
    I figured it out. Your post was a great help.
     
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