A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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![**Avicenna Major Insurance Policy Analysis**
Avicenna, a prominent insurance company, offers five-year life insurance policies to individuals aged 65. If the policyholder passes away before reaching the age of 70, the company will pay $27,400 to the policy's beneficiary. The executives at Avicenna are contemplating selling these policies for $765 each. The probability of a policyholder dying before age 70 is 3%, while the probability of surviving until age 70 is 97%.
The core question here is:
*If the executives at Avicenna know that they will sell many of these policies, should they expect to make or lose money from offering them? How much?*
To address this question, we need to consider the price of the policy and the expected value of the payouts.
**Options to Analyze:**
1. **Avicenna can expect to make money from offering these policies.**
- In the long run, they should expect to make \_\_\_ dollars on each policy sold.
2. **Avicenna can expect to lose money from offering these policies.**
- In the long run, they should expect to lose \_\_\_ dollars on each policy sold.
3. **Avicenna should expect to neither make nor lose money from offering these policies.**
### Calculation of Expected Value:
This section involves calculating the expected monetary outcome for Avicenna on average per policy sold. This is determined by considering the probabilities and the associated costs/revenues:
- **Probability of paying out $27,400 (death before 70):** 3%.
- **Probability of not paying out (alive at 70):** 97%.
- **Revenue from selling each policy:** $765.
The expected cost to Avicenna for each policy sold is:
\[ \text{Expected Payout} = (0.03 \times 27,400) + (0.97 \times 0) = 822 \]
Then, to determine the net gain or loss:
\[ \text{Net Gain/Loss} = \text{Revenue} - \text{Expected Payout} \]
\[ \text{Net Gain/Loss} = 765 - 822 = -57 \]
Therefore, in the long run, Avicenna can expect to lose $57 on each policy sold, matching the second option:
- **Avicenna can expect to lose money from offering these policies.**](https://content.bartleby.com/qna-images/question/424746dd-29d3-476a-868c-5a06ada19580/97ee05e2-d189-48b9-8973-87981212973f/kcu4inm_processed.jpeg)
Transcribed Image Text:**Avicenna Major Insurance Policy Analysis**
Avicenna, a prominent insurance company, offers five-year life insurance policies to individuals aged 65. If the policyholder passes away before reaching the age of 70, the company will pay $27,400 to the policy's beneficiary. The executives at Avicenna are contemplating selling these policies for $765 each. The probability of a policyholder dying before age 70 is 3%, while the probability of surviving until age 70 is 97%.
The core question here is:
*If the executives at Avicenna know that they will sell many of these policies, should they expect to make or lose money from offering them? How much?*
To address this question, we need to consider the price of the policy and the expected value of the payouts.
**Options to Analyze:**
1. **Avicenna can expect to make money from offering these policies.**
- In the long run, they should expect to make \_\_\_ dollars on each policy sold.
2. **Avicenna can expect to lose money from offering these policies.**
- In the long run, they should expect to lose \_\_\_ dollars on each policy sold.
3. **Avicenna should expect to neither make nor lose money from offering these policies.**
### Calculation of Expected Value:
This section involves calculating the expected monetary outcome for Avicenna on average per policy sold. This is determined by considering the probabilities and the associated costs/revenues:
- **Probability of paying out $27,400 (death before 70):** 3%.
- **Probability of not paying out (alive at 70):** 97%.
- **Revenue from selling each policy:** $765.
The expected cost to Avicenna for each policy sold is:
\[ \text{Expected Payout} = (0.03 \times 27,400) + (0.97 \times 0) = 822 \]
Then, to determine the net gain or loss:
\[ \text{Net Gain/Loss} = \text{Revenue} - \text{Expected Payout} \]
\[ \text{Net Gain/Loss} = 765 - 822 = -57 \]
Therefore, in the long run, Avicenna can expect to lose $57 on each policy sold, matching the second option:
- **Avicenna can expect to lose money from offering these policies.**
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