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.