Question

An insurance policy sells for $1200. Based on past data, an average of 1 in 50 policyholders will file a $10,000 claim, an average of 1 in 250 policyholders will file a $40,000 claim, and an average of 1 in 400 policyholders will file an $80,000 claim. Find the expected value (to the company) per policy sold. If the company sells 10,000 policies, what is the expected profit or loss?

Answer 1

x	-8800	-38800	-78800	1200
p	1/50	1/250	1/400	1947/2000

P(1200) = 1 - 1/50 - 1/250 - 1/400 = 1947/2000

And when there is a claim of $10000 then that's a loss of 8800 for company as company got $1200 as premium and paid $10000 hence net is 1200 - 10000 = -8800

And so on we will get -78800 and -38800

Hence the expected value is $640 profit per policy for the company.

If company sells 10000 policies then total profit = 640*10000 = $6400000.