A 40-year-old man in the U.S. has a 0.249% risk of dying during the next year . An insurance company charges $300 per year for a life-insurance policy that pays a $100,000 death benefit. What is the expected value for the person buying the insurance? Round your answer to the nearest dollar.

Expected Value: $ for the year

The expected value for the person buying the insurance can be calculated by considering the two possible outcomes:

1. **The person survives** (probability of survival): The person loses the premium paid to the insurance company.
2. **The person dies** (probability of death): The person receives the death benefit of $100,000, but loses the premium.

### Step-by-step calculation:

1. **Probability of death**: 0.249% = 0.00249
2. **Probability of survival**: 1 - 0.00249 = 0.99751
3. **Cost of premium**: $300
4. **Death benefit**: $100,000

Now, let's calculate the expected value $ E(X) $.

\[
E(X) = (\text{Probability of death} \times \text{Net gain if death occurs}) + (\text{Probability of survival} \times \text{Net gain if survival occurs})
\]

- **Net gain if death occurs**: $100,000 - $300 = $99,700
- **Net gain if survival occurs**: $-300 (since the person only pays the premium with no benefit)

Thus:

\[
E(X) = (0.00249 \times 99,700) + (0.99751 \times -300)
\]

\[
E(X) = (248.253) + (-299.253)
\]

\[
E(X) = -51
\]

### Conclusion:
The expected value for the person buying the insurance is **- $51** for the year (rounded to the nearest dollar).

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Would you like more details or have any questions?

Here are 5 related questions you might find interesting:
1. How would the expected value change if the premium were $400?
2. What is the insurance company's expected value for this policy?
3. How does the risk of death impact the premium charged by insurance companies?
4. What is the break-even premium for this insurance policy?
5. How would a different death benefit (e.g., $200,000) affect the expected value?

**Tip**: Expected value helps assess whether a financial decision is fair or beneficial over time, especially in insurance and gambling scenarios.

A 40-year-old man in the U.S. has a 0.249% risk of dying during the next year. An insurance company charges $300 per year for a life-insurance policy that pays a $100,000 death benefit. What is the expected value for the person buying the insurance? Round your answer to the nearest dollar.

Calculate the expected value for a 40-year-old man buying a life insurance policy with a 0.249% chance of death. Learn the step-by-step breakdown of the expected value formula, risk analysis, and how probability influences decision-making in life insurance. Suitable for Grades 10-12.

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