SOLUTION: I need help with this one, Thanks, Insurance I. Suppose a company charges an annual premium of $500 for a fire insurance policy. In case of a fire claim, the company wi

Question 1040073: I need help with this one,
Thanks,

Insurance I. Suppose a company charges an annual premium of $500 for a fire insurance policy. In case of a fire claim, the company will pay out an average of $100,000. Based on actuarial studies, it determines that the probability of a fire claim in a year is 0.004.
What is the expected annual profit of a fire insurance policy for the company?
(Fill in the blank below and give your answer as a whole number.)
The expected annual profit per policy is $.

What annual profit can the company expect if it issues 1000 policies?
(Fill in the blank below and give your answer as a whole number.)
The expected annual profit if it issues 1000 policies is $.

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
E(x)=x*p(x)
+ side is 500*0.996, which is probability nothing will happen.
That is $498
- side is a claim, which is 100,000*0.004=$400
The average profit is $98 on each policy sold.
------------------
One would expect a profit of $98000 for 1000 policies.
Let's look at expected value
500*996=498,000
minus 4 fires at $100,000 each, which is $400,000. The profit is the difference, or $98,000
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