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I found this question rather interesting and very confusing, check it out

an insurance company classifies its customers as either high risk 5% of people, medium risk 25% of people, and low risk 70% of people. now the probability of a high risk customer making a claim in the first year is 75%, medium risk 45% and low risk is 5%, now if the companies prcocedure is to place new customers in high risk,and if they dont make a claim in first year then they will be placed into medium risk in the second year and if they dont make a claim in the second year then they will be placed into low risk.

firstly what is the probability of a customer going through this procedure if

actually he is a low risk customer.

secondly what is the probability of a customer going through this procedure if actually he is a high risk customer.

lastly would such a procedure be fair on customers?

I was only able to do the first bit, dont know if I am correct, please correct me if im wrong

P(Procedure|low risk)=P(does not make claim&high risk)+

P(does not make claim&medium risk)=0.05*0.25+0.25*0.55=0.15

steven

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# Probability and insurance

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