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Math Help - Probability problem

  1. #1
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    Probability problem

    A doctor says that a infant who predominantly turns the head to the
    right will be right-handded and the one who turns the head to the left
    will be left-handed. The newborn baby girl turned her head to the left.
    Given that 90% of the population is right-handed, what is the probability
    of baby being right handed if the test is 90% accurate ? What if it is
    80% accurate ?

    I got 0.5 for the first question and 0.6923 for the second, is this correct?
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  2. #2
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    I think you need to use the Bayes formula.

    [P(A)P(ClA)]/[(P(A)P(ClA))(P(B)P(ClB))...]

    P(A) = .9
    P(B) = .1
    P(ClA) = .9
    P(ClB) = .1

    [(.9)(.9)]/[(.9)(.9)+(.1)(.1)]
    .81/.82
    98.78%


    P(A) = .9
    P(B) = .1
    P(ClA) = .8
    P(ClB) = .2

    [(.9)(.8)]/[(.9)(.8)+(.1)(.2)]
    .72/.74
    97.3%

    Oops, I don't think this is right.
    Last edited by dkmathguy; April 12th 2010 at 12:11 AM.
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  3. #3
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    Quote Originally Posted by bsqrs View Post
    A doctor says that a infant who predominantly turns the head to the
    right will be right-handded and the one who turns the head to the left
    will be left-handed. The newborn baby girl turned her head to the left.
    Given that 90% of the population is right-handed, what is the probability
    of baby being right handed if the test is 90% accurate ? What if it is
    80% accurate ?

    I got 0.5 for the first question and 0.6923 for the second, is this correct?
    I get the same, to four decimal places (actually I get the exact answers of 1/2 and 9/13).
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