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baye stheorem

  • 05-12-2011 8:23pm
    #1
    eoins23456
    Registered Users, Registered Users 2 Posts: 603 ✭✭✭


    There are 3 drugs available for a common disease.Drug 1 is cheaper than Drug 2 which is,in turn,cheaper than Drug 3.A doctor will initially prescribe Drug 1.The probability that Drug 1 proves effective is .4.If drug 1 is not effective the doctor will prescribe drug 2 which is effective with probability .6.If neither drug 1 nor drug 2 are effective the doctor will prescribe drug 3 which is effective with probability .8. let c be the event that treatment is effective(ie at least one of the drugs proves to be effective).let d1 be the event that drug i was the first to be found effective ont he patient.

    calculate p(c)
    p(d1|c) p(d2|c) p(d3|c)

    so p(c)= 1-( (1-.4)(1-.6)(1-.8))=.952
    using bayes formula p(B|A)=(P(A|B)* P(B))/(p(A)

    p(d1|c)= (1*.4)/.952 = .4201
    p(d2|c) = (1*.6)/.952 = .63
    p(d3|c)= (1*.8)/.952 = .84



    Is this right?


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