(adsbygoogle = window.adsbygoogle || []).push({}); 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

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# Partition Theorem

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