How much should the company charge for the policy if it requires that the expected profit per policy be $80?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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An insurance company issues a one-year $1,000 policy insuring against an occurrence A that historically happens to 7 out of every 100 owners of the policy. Administrative fees are $25 per policy and are not part of the company's "profit." How much should the company charge for the policy if it requires that the expected profit per policy be $80? [HINT: If C is the premium for the policy, the company's "profit" is C − 25 if A does not occur, and C − 25 − 1,000 if A does occur.]

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here given,

An insurance company issues a one-year $1,000 policy insuring against an occurrence A that historically happens to 7 out of every 100 owners of the policy

probability of A = p(A) = 7/100 = 0.07

probability of A' = 1-p(A) = 0.93

here x= profit for company

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