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.