A 40-year-old man in the U.S. has a 0.24% risk of dying during the next year . An insurance company charges $270 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 a person buying life insurance is calculated by considering the two possible outcomes:

1. **If the person dies**: They will receive the benefit of $100,000, but they paid $270 for the insurance.
2. **If the person does not die**: They lose the $270 paid for the insurance, but receive no benefit.

The expected value (EV) is given by:

\[
\text{EV} = P(\text{death}) \times (\text{benefit} - \text{premium}) + P(\text{no death}) \times (-\text{premium})
\]

Where:
- $ P(\text{death}) = 0.0024 $ (0.24% chance of dying),
- $ P(\text{no death}) = 1 - P(\text{death}) = 0.9976 $ (99.76% chance of not dying),
- Benefit = $100,000,
- Premium = $270.

Let’s compute the expected value step by step.

\[
\text{EV} = (0.0024 \times (100,000 - 270)) + (0.9976 \times (-270))
\]

I’ll calculate that.The expected value for the person buying the life insurance is $-30$ dollars for the year. This means that, on average, the person can expect to lose $30 over the course of the year by purchasing the policy.

Would you like more details on how this was calculated, or do you have any further questions?

Here are 5 related questions to explore:
1. How does the probability of death affect the expected value?
2. What happens to the expected value if the premium is increased or decreased?
3. How would a longer policy term impact the expected value?
4. Can the expected value ever be positive for the insured person?
5. What role does risk play in setting insurance premiums?

**Tip**: Insurance companies set premiums so that the expected value is negative for the insured person, ensuring a profit over many policies.

A 40-year-old man in the U.S. has a 0.24% risk of dying during the next year. An insurance company charges $270 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.

Find the expected value of a life insurance policy where a 40-year-old man has a 0.24% risk of dying during the next year. This problem explores key probability concepts and the expected value formula to determine the financial outcome of buying a $100,000 policy with a $270 premium. Ideal for students in Grades 10-12.

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