Problem 6. This problem is based on Probl 5a p 1 (a) Let {E.bEj be purttsm the L

Question

Problem 6. This problem is based on Probl 5a p 1 (a) Let {E.bEj be purttsm the Law of Total Phobability as it apelis to the partitis ( (b) Au insurance and 70% are low-risk iven that a clent is hichrisk, is bused on Phob St p 117 in the tosthbosk a purtition of the smpike spuce S, and ket F he ans evest State chanee that they wi there is a 3 is mnhum-risk, there is a 2% chaar that they will file a eksim: and geven that acivet is kwnk, there is a 1% chance that they will file a claim. Using the law of Total Proability, oakulate the probability that a randomly chosen client hles a chaim ) Givm that a clikent Slkes a clhaim, calculate the prolabhility that the client is high-risk

Explanation / Answer

a) as law of total probability states that probability of an event is marginal addition of its conditional probability.

hence P(F) =P(E1)*P(F|E1)+P(E2)*P(F|E2)+P(E3)*P(F|E3)

b)probability that a randomely chosen client files a claim =high risk and claim+ medium risk and claim+low risk and claim =0.1*0.03+0.2*0.02+0.7*0.01=0.014

c)probability that client is at high risk given client files a claim

=P(high risk and claim)/P(claim)=0.1*0.03/0.014=0.2143

please revert for any clarification required

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