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This problem is asking for the **expected value** for a person buying a life-insurance policy. The expected value ($E$) in this context is the average financial outcome for the buyer, considering both the chance of dying (and receiving the $100,000 benefit) and the chance of surviving (and only losing the $300 premium).

### Given Information:
- The probability of dying within a year is 0.24%, or $0.0024$.
- The death benefit payout is $100,000.
- The insurance premium is $300.
- The probability of surviving is $1 - 0.0024 = 0.9976$.

### Calculation:

1. **Expected value for dying**: If the person dies, they (or their family) receive $100,000. Since they have already paid $300 for the premium, the net gain is $100,000 - 300 = 99,700$.
   
   Probability of this outcome: 0.0024.

   So, the expected value for dying is:
   \[
   E(\text{dying}) = 99,700 \times 0.0024 = 239.28
   \]

2. **Expected value for surviving**: If the person survives, they do not receive any payout but they lose the $300 premium.

   Probability of this outcome: 0.9976.

   So, the expected value for surviving is:
   \[
   E(\text{surviving}) = -300 \times 0.9976 = -299.28
   \]

3. **Total Expected Value**: Now, sum these two expected values:
   \[
   E = E(\text{dying}) + E(\text{surviving}) = 239.28 + (-299.28) = -60.00
   \]

### Answer:
The expected value for the person buying the insurance is **$-\$60.00$**.

Would you like further details or have any questions? Here are five related questions to consider:

1. What is the significance of a negative expected value in decision-making?
2. How would the expected value change if the death benefit were increased?
3. What happens to the expected value if the probability of dying increases?
4. Why does the expected value only consider probabilities and not personal preferences?
5. How do insurance companies use expected value to set premiums?

**Tip:** In expected value problems, always identify all possible outcomes, their corresponding probabilities, and the associated gains or losses.

A 40-year-old man in the U.S. has a 0.24% 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 cent. Be careful with negative signs.

This problem calculates the expected value for a 40-year-old U.S. male purchasing life insurance. The premium is $300 for a $100,000 benefit, with a 0.24% chance of death. Using probability theory, the solution shows how the total expected value is -$60.00, providing insights into financial decision-making with life insurance.

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