An insurance company sells a one-year term life insurance policy to an 80-year-old woman. The woman pays a premium of $1000. If she dies within one year, the company will pay $18,500 to her beneficiary. According to the company's statistics department, the probability that an 80-year-old woman will be alive one year later is 0.9581. Find the expected value of the insurance company's profit.

The profit of the company will be $224.85

Step-by-step explanation:

Let the equation of profit be termed as E(x)

we are given

amount of purchasing the policy (let a)= $1000

probability that women will live for at least 1  year (let b) = 0.9581

amount lost by insurance company if the women dies (let c) = 18,500-1000 = 17,500

the probability woman dies within one year (let d) = 1-0.9581=0.0419

the equation will be

E(x) of profit= a*b - c*d = 1000*0.9581 - 17500*0.0419

                    = 958.1 - 733.25

                    =  224.85

step-by-step explanation:

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