An insurance company gives older customers a benefit if they need a certain medi

Question

An insurance company gives older customers a benefit if they need a certain medical procedure. 40% of their custo ners are in age group 1 and 60% of their customers are in age group II. It is known that customers in age group II are two times more likely to get the benefit than customers in age group I. Also, given a need for the medical procedure, the company pays customers in age group I a benefit of $300 and customers in age group II a benefit of $500. Given that a random customer gets the benefit compute the amount the insurance company expects to pay the customer

Explanation / Answer

Pr(Customer in age group I) = 0.40

Pr(Customer in age group II) = 0.60

Let say probability in age group I to get benifit = p then probability in age group II to get insurance benifit = 2p

so Expected amount the insurance company to pay the customer given that a random customer gets the benifit .

Pr( Random custome gets the profit) = Pr(Person from Age Group I) * Pr(He/ she will get profit) + Pr(Person from age group II) * Pr(He ' she will get profit)

= 0.4 * p + 0.6 * 2p = 1.6p

Expected benifit a customer gets = 0.4 * p * 300 + 0.6 * 2p * 500 = 120 p + 600 p = 720 p

so,

Expected amount the insurance company to pay the customer given that a random customer gets the benifit .

= 720p/ 1.6p = $ 450

so insurance company expects to pay $ 450 to random customer if he gets the benift.

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