The probability that a 22-year-old female in the U.S. will die within one year is approximately 0.00044. If an insurance company sells a one-year, $30,000 life insurance policy to such a person for $135, what is the company's expectation? (Round your answer to the nearest dollar.)$
Question
The probability that a 22-year-old female in the U.S. will die within one year is approximately 0.00044. If an insurance company sells a one-year, 135, what is the company's expectation? (Round your answer to the nearest dollar.)$
Solution
The expectation of the insurance company can be calculated by finding the expected profit from the policy. This is done by subtracting the expected loss from the premium charged.
Step 1: Calculate the expected loss The expected loss is the product of the probability of the event (in this case, the death of the policyholder) and the payout if the event occurs.
Expected Loss = Probability of death * Payout = 0.00044 * 13.2
Step 2: Calculate the expected profit The expected profit is the premium charged minus the expected loss.
Expected Profit = Premium - Expected Loss = 13.2 = $121.8
So, the company's expectation is approximately $122 when rounded to the nearest dollar.
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