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March 25, 2017

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Musical styles other than rock and pop are becoming more popular. A survey of college students finds that 48% like country music, 30% like gospel music, and 10% like both. What is the conditional probability (±0.01) that a student likes gospel music, given that he or she likes country music

  • statistics - ,

    Conditional probability of A given B is given by
    P(A|B)=P(A∩B)/P(B)
    C=country, P(C)=0.48
    G=gospel, P(G)=0.30
    C∩G=both, P(C∩G)=0.10
    P(gospel given country)
    =P(G|C)
    =P(G∩C)/P(C)
    =0.10/0.48
    =0.21

  • statistics - ,

    p(c)=0.48
    p(g)=0.30
    p(cng)=0.10

    p(CuN)=0.48+0.30-0.10
    =0.68

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