SOLUTION: Suppose a company charges a premium of $150 per year for an insurance policy for storm damage to roofs. Actuarial studies show that in case of a storm, the insurance company will p

Question 1195336: Suppose a company charges a premium of $150 per year for an insurance policy for storm damage to roofs. Actuarial studies show that in case of a storm, the insurance company will pay out an average of $8000 for damage to a composition shingle roof and an average of $12,000 for damage to a shake roof. They also determine that out of every 10,000 policies, there are 7 claims per year made on composition shingle roofs and 11 claims per year made on shake roofs. What is the company’s expected value (i.e., expected profit) per year of a storm insurance policy? What annual profit can the company expect if it issues 1000 such policies?
Determine the probability of a composition shingle roof claim out of 10,000 = ?
Determine the probability of a shake roof claim out of 10,000 = ?

Answer by ElectricPavlov(122) (Show Source): You can put this solution on YOUR website!
**1. Calculate Probabilities:**
* **Probability of a composition shingle roof claim:** 7 claims / 10,000 policies = 0.0007
* **Probability of a shake roof claim:** 11 claims / 10,000 policies = 0.0011
**2. Calculate Expected Payout per Policy**
* **Expected payout for composition shingle roof claims:**
* Probability * Payout amount = 0.0007 * $8000 = $5.60
* **Expected payout for shake roof claims:**
* Probability * Payout amount = 0.0011 * $12,000 = $13.20
* **Total expected payout per policy:** $5.60 + $13.20 = $18.80
**3. Calculate Expected Profit per Policy**
* **Expected profit per policy:** Premium - Expected payout = $150 - $18.80 = $131.20
**4. Calculate Expected Annual Profit for 1000 Policies**
* **Expected annual profit:** Expected profit per policy * Number of policies = $131.20 * 1000 = $131,200
**Therefore:**
* The company's expected profit per year of a storm insurance policy is $131.20.
* The expected annual profit for 1000 such policies is $131,200.

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