Question

An insurance policy sells for ​$1200. Based on past​ data, an average of 1 in 25 policyholders will file a ​$20,000 ​claim, an average of 1 in 200 policyholders will file a ​$30,000 ​claim, and an average of 1 in 250 policyholders will file a ​$70,000 claim. Find the expected value​ (to the​ company) per policy sold. If the company sells 20,000 ​policies, what is the expected profit or​ loss?

Answer 1

The expected value of the insurance policy to the company per policy sold is -$80, indicating an expected loss. If the company sells 20,000 policies, the expected loss would be $1,600,000.

Step-by-step explanation:

The question asks us to calculate the expected value of an insurance policy to the company and the expected profit or loss when 20,000 policies are sold. To find the expected value per policy, we will use the probabilities of the different claims and the amounts for each claim. With 1 in 25 policyholders filing a $20,000 claim, 1 in 200 filing a $30,000 claim, and 1 in 250 filing a $70,000 claim, we calculate as follows:

1. Probability of a $20,000 claim: 1/25
2. Probability of a $30,000 claim: 1/200
3. Probability of a $70,000 claim: 1/250

Expected value per policy = (1/25) × $20,000 + (1/200) × $30,000 + (1/250) × $70,000 - $1,200 (cost of policy) = -$80 (per policy).

If the company sells 20,000 policies, the expected total value = 20,000 × -$80 = -$1,600,000, which indicates the company is expected to incur a loss of $1,600,000.