Solved: An insurance company writes a policy to the effect

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QUESTION:

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 so that its expected profit will be 10 percent of A?

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QUESTION:

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 so that its expected profit will be 10 percent of A?

ANSWER:

Step 1 of 2

The event  occurs with probability . Let  be the amount charged by the insurance company. This amount must be paid even if event  occurs or not. So, expected profit is

(Income -expected profit)

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