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An insurance company writes a policy to the effect that an amount of money A must be paid if some event E occurs within a year. If the company estimates that E will occur within a year with probability p, what should it charge the customer in order that its expected profit will be 10 percent of A?

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Answer:

(0.1 + p)A

Step-by-step explanation:

The expected value paid by the insurance company is determined by the amount paid incase E happens multiplied by the likelihood of E occurring:

[tex]E(E) = p*A[/tex]

The profit is given by the amount charged subtracted by the expected value of the policy, if the desired profit is 0.10A, the amount charged (C) must be:

[tex]0.10A = C - pA\\C= (0.1+p)A[/tex]

The company should charge (0.1 + p)A.

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