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Part 1
There is a 0.9983 probability that a randomly selected 32​-year-old male lives through the year. A life insurance company charges ​$196 for insuring that the male will live through the year. If the male does not survive the​ year, the policy pays out ​$110 comma 000 as a death benefit.  From the perspective of the 32​-year-old ​male, what are the monetary values corresponding to the two events of surviving the year and not​ surviving?
The value corresponding to surviving the year is ​$
  
enter your response here.
The value corresponding to not surviving the year is ​$

Let's calculate the monetary values for each scenario: surviving and not surviving the year.

### 1. **Surviving the year:**
- If the male survives the year, the insurance company does not pay any benefit.
- The cost for the insurance policy is $196 (already paid).
- Therefore, the monetary value of surviving the year is **–$196** (since the male pays this amount for the insurance and gets nothing in return).

So, the value corresponding to surviving the year is:  
\[
\boxed{-196}
\]

### 2. **Not surviving the year:**
- If the male does **not** survive the year, the policy pays out $110,000 as the death benefit.
- He still paid $196 for the insurance policy, but since the death benefit is $110,000, the net value would be:
\[
110,000 - 196 = 109,804
\]

So, the value corresponding to not surviving the year is:  
\[
\boxed{109,804}
\]

Would you like to see further details or ask any questions?

Here are 5 related questions to expand on the information:
1. What is the expected value of the insurance for the male based on probabilities?
2. How does this calculation change if the probability of survival changes?
3. What are the odds of the company profiting from this policy?
4. How do life insurance companies calculate premiums to ensure profitability?
5. Can the value of insurance be considered from a risk management perspective?

**Tip:** In expected value problems, always account for both the cost and the payout in each scenario to get a comprehensive understanding.

There is a 0.9983 probability that a randomly selected 32​-year-old male lives through the year. A life insurance company charges $196 for insuring that the male will live through the year. If the male does not survive the year, the policy pays out $110,000 as a death benefit. From the perspective of the 32​-year-old ​male, what are the monetary values corresponding to the two events of surviving the year and not​ surviving?

Explore the probability of survival and the monetary values associated with life insurance for a 32-year-old male. This problem uses key concepts of probability and risk analysis, focusing on expected values and calculating the net monetary values of different outcomes. Suitable for students in Grades 10-12.

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