(a) Let {E_1, E_2, E_3} be a partition of the sample space S, and let F be any e
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Question
(a) Let {E_1, E_2, E_3} be a partition of the sample space S, and let F be any event. State the Law of Total Probability as it applies to the partition {E_1, E_2, E_3} and the event F. (b) An insurance company finds that 10% of its clients are high-risk, 20% are medium-risk, and 70% are low-risk. Given that a client is high-risk, there is a 3% chance that they will a claim given that a client is medium-risk, there is a 2% chance that they will file a claim. Using the Law of Total Probability, calculate the probability that a randomly chosen client files is claim. (c) Given that a client files a claim, calculate the probability 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 =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 =0.1*0.03/0.014=0.2143
please revert for any clarification required
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