An insurance policy sells for $1200. Based on past data, an average of 1 in 100 policyholders will file a $10 comma 000 claim, an average of 1 in 250 policyholders will file a $40 comma 000 claim, and an average of 1 in 400 policyholders will file an $80 comma 000 claim. Find the expected value (to the company) per policy sold. If the company sells 30 comma 000 policies, what is the expected profit or loss?

Expected Value = $740

Expected profit = $22.2m

Explanation:

We can easily calculate the expected value and expected profit/loss in this situation by some minor working

Expected values = Expected Claim - per policy cost

Expected profit/loss = (Expected claim - per policy cost) x number of policies

As you can see per policy cost and no of policies are given in the question data we just need to find expected claim for calculation of expected profit or loss and expected value

Expected Claim = (1/100x$10,000) + (1/250x$40,000) + (1/400x$80,000)

Expected Claim = 100 + 160 + 200

Expected Claim = 460

Now we have a value of expected claim lets put it into Expected profit/loss formula and expected value formula

Expected value = 460-1200

Expected value = - 740

-$740 is the value per policy

Expected profit/loss = (460 - $1200 per policy) x 30,000

Expected profit or loss = - 22,200,000

Expected loss to the customer = - $22.2 m

Expected profit for the company = $22.2m