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Simple Statistical Question

  1. Jan 20, 2006 #1
    Hello Gentlemen,

    Here's a statistical question for you:

    A man and a woman mate to produce a child that either has blue eyes (B) or green eyes (b), where blue eyes are dominant to green eyes.

    As you remember from biology, there are 3 different possibilities for the genotype - BB, Bb, or bb.

    The probabilities are 1:2:1 for BB:Bb:bb.

    Thus, the chance for the child to have blue eyes is 3/4 and green eyes is 1/4.

    Ok, I'm getting to the question now. The couple decides to have 2 children. What is the probability that the 2 children will have the same appearance and be of the same sex?

    Here's what I think the answer is:

    green eyes: (0.5*0.5*0.25*0.25)*100% = 1.5%
    blue eyes:
    (0.5*0.5*0.75*0.75)*100% = 14.1%

    Is this correct? Thanks.
  2. jcsd
  3. Jan 20, 2006 #2


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    Prob(same sex) = P(boy)2+P(girl)2 = 2(0.5)2 = 2*0.25 = 0.5.

    Blue boys = (0.5*0.75)2 = Blue girls

    green boys = (0.5*0.25)2 = green girls

    Blue boys or blue girls = 2(0.5*0.75)2
    green boys or green girls = 2(0.5*0.25)2
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