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Homework Help: Partition Theorem

  1. Jan 10, 2012 #1
    1. The problem statement, all variables and given/known data
    Assume that it is appropriate to transfer the probabilities IP(F|L) and IP(F|T) from the police context to the insurance context.
    Define the following new events for the insurance context:
    L = “insurance claimant is lying”;
    T = “insurance claimant is truthful”;
    F = “insurance claimant failed lie-detector test on phone”;
    P = “insurance claimant passed lie-detector test on phone”.
    An insurance company finds that a massive 52.5% of claimants fail the liedetector
    test on the phone. What is the probability that a claimant is actually
    lying?

    IP(F) = 0.525 IP(P) = 1-0.525=0.475
    IP(F|L)=0.38 IP(F|T)=0.23
    IP(P|L)=0.14 IP(P|T)=0.25

    2. Relevant equations
    Bayesian TheoremP(B |A) = P(A|B)P(B)/ P(A)
    IP(L) = IP((L|F) [itex]\cap[/itex] (L|P))


    3. The attempt at a solution
    IP(L|F)=(0.38*0.525) / (0.38*0.525+0.23*0.525)=0.1995/0.32025=0.62
    IP(L|P)=(0.14*0.475) / (0.14*0.475+0.25*0.475)=0.0665/0.18525 = 0.36

    IP(L) = IP((L|F) [itex]\cap[/itex] (L|P))
    = IP(L|F) * IP(L|P)
    = 0.62 * 0.36 = 0.2232

    is my workings right? I'm kind of worried that I used the wrong formula to work out IP(L), so it would be nice if someone could double check that part too
    thanks
     
  2. jcsd
  3. Jan 10, 2012 #2

    lanedance

    User Avatar
    Homework Helper

    Though I haven't checked numbers, your use of Bayes to get IP(L|F) and IP(L|P) is on the right track, and given the results show someone who fails the test is likely to be lying (62%) or someone who passes the test is unlikely to be lying (36%) is encouraging

    I don't understand what you've done in the last step however. I would notice (or assume) that the events P&F span the entire probabilty universe, and use the following:

    IP(L) = IP(L|F)IP(F) + IP(L|P)IP(P)
     
    Last edited: Jan 10, 2012
  4. Jan 10, 2012 #3
    you are right, I just figured it out about half an hour ago. I knew I had implied some of the formula wrongly.

    Thanks for confirming that with me!
     
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