There is a 0.9989 probability that a randomly selected 29-year-old male lives through the year. A life insurance company charges $197 for insuring that the male will live through the year. If the male does not survive the year, the policy pays out $100,000 as a death benefit.

Required:
a. From the perspective of the 29-year-old male, what are the monetary values corresponding to the two events of surviving the year and not surviving?
b. If the 29-year-old male purchases the policy, what is his expected value?
c. Can the insurance company expect to make a profit from many such policies? Why?

Answers

Answer 1

a. Surviving the year: $197; Not surviving the year: $100,000

b. Expected value: $306.78

c. The insurance company can expect to make $86.49 in profit per policy.

We have,

a.

From the perspective of the 29-year-old male:

Surviving the year:

The monetary value is the cost of the insurance premium, which is $197.

Not surviving the year:

The monetary value is the death benefit paid out by the policy, which is $100,000.

b.

To calculate the expected value for the 29-year-old male, multiply the probability of each event by its corresponding monetary value and sum them up:

Expected Value = (Probability of Surviving * Monetary Value of Surviving) + (Probability of Not Surviving * Monetary Value of Not Surviving)

= (0.9989 * $197) + (0.0011 * $100,000)

= $306.78

c.

Expected Premium Revenue

= Probability of Surviving * Premium Amount

= 0.9989 * $197

≈ $196.49

Expected Payout

= Probability of Not Surviving * Death Benefit

= 0.0011 * $100,000

≈ $110

Profitability

= Expected Premium Revenue - Expected Payout

= $196.49 - $110

≈ $86.49

Since the expected premium revenue exceeds the expected payout, the insurance company can expect to make a profit from many such policies.

In this scenario, the insurance company can expect to make $86.49 in profit per policy.

Therefore,

a. Surviving the year: $197; Not surviving the year: $100,000

b. Expected value: $306.78

c. The insurance company can expect to make $86.49 in profit per policy.

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Answer 2

a. From the perspective of the 29-year-old male:

Surviving the year: The cost of insurance is $197.

Not surviving the year: The policy pays out a death benefit of $100,000.

b. The 29-year-old male's expected value is -$86.8013, indicating a potential loss.

c. Yes, the insurance company can expect to make a profit. The expected value is negative, meaning the company collects more in premiums than it pays out on average.

a. From the perspective of the 29-year-old male:

Surviving the year: The cost of insuring that the male will live through the year is $197.

Not surviving the year: The policy pays out a death benefit of $100,000.

b. To calculate the expected value for the 29-year-old male, we need to consider the probabilities of each event and their corresponding monetary values.

Expected Value = (Probability of surviving * Monetary value of surviving) + (Probability of not surviving * Monetary value of not surviving)

Probability of surviving = 0.9989

Monetary value of surviving = -$197 (since this represents the cost of insurance)

Probability of not surviving = 1 - Probability of surviving = 1 - 0.9989 = 0.0011

Monetary value of not surviving = $100,000

Expected Value = (0.9989 * -$197) + (0.0011 * $100,000)

Expected Value = -$196.8013 + $110

Expected Value = -$86.8013

Therefore, the expected value for the 29-year-old male is approximately -$86.8013.

c. The insurance company can expect to make a profit from many such policies because the expected value is negative (-$86.8013). The cost of insuring the male is $197, but the expected value is significantly less. This means that on average, the insurance company will collect more in premiums than it pays out in claims, resulting in a profit. The small probability of not surviving the year and the high payout of $100,000 contribute to the insurance company's ability to make a profit by spreading the risk among many policyholders.

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