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Math Help - conditonal probability question

  1. #1
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    Unhappy conditonal probability question

    In a Spam filter design, following events are defined,

    s: email is spam A1=email contains string "cheapest"
    A2=email contains string "lottery" A3=email contains string "credit"

    it is found,
    P(S) =0.2
    P(A1|S)=0.2 P(A2|S)=0.4 P(A3|S)=0.2
    P(A1|S')=0.05 P(A2|S')=0.1 P(A3|S')=0.01

    conditional on S, assume A1 , A2 , A3 are independent.

    find the probability that email is spam if,

    1)A1 occurs (p1) 2) both A1 and A2 occur (p2)
    3)A1,A2,A3 occur (p3) 4)explain why p3>p2>p1



    -------------------------------
    i solved 1st one using Bayes theorem and i got 0.5 as the answer.

    i need help for 2nd ans 3rd parts.

    i couldn't get an answer for 2nd part, I got 0.25 when i assumed (s Ʌ A1) and (S Ʌ A2) which must be wrong because it should be greater than 0.5

    by the way is it wrong to assume (s Ʌ A1) and (S Ʌ A2) are independent when A1 and A2 are independent?
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  2. #2
    MHF Contributor
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    edit wrong answer removed
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