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In a survey to determine the opinions of Americans on health insurers, 400 baby boomers and 600 pre-boomers were asked this question: Do you believe that insurers are very responsible for high health costs? Of the baby boomers, 232 answered in the affirmative, whereas 192 of the pre-boomers answered in the affirmative. If a respondent chosen at random from those surveyed answered the question in the affirmative, what is the probability that he or she is a baby boomer? A pre-boomer? (Round your answers to two decimal places.)

baby boomer ?
pre-boomer ?

  • math -

    Let events
    B=baby boomer
    ~B=pre-boomer (complement of B)
    A=answered in affirmative

    then by the law of total probability:
    P(A)=P(A∩B)+P(A∩~B)
    =P(A|B)*P(B)+P(A|~B)*P(~B)
    =232/400*(400/1000)+192/600*(600/1000)
    =0.424

    using Bayes theorem,
    P(B|A)=P(A|B)P(B)/P(A)
    =(232/400)*0.4/(0.424)
    =0.5472
    or
    P(boomer|affirmative answer) = 0.5472

    I'll leave it to you to find
    P(pre-boomer|affirmative answer) by finding the complement.

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