What is the expected value? The expected value is dollars.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![### Life Insurance Expected Value Calculation
---
#### Problem Statement:
Assume that the probability of a 25-year-old male living to age 26, based on mortality tables, is 0.993. If a 16,000 dollar one-year term life insurance policy on a 25-year-old male costs 100 dollars, what is its expected value?
---
#### Calculation:
**What is the expected value?**
The expected value is \[ ______ \] dollars.
---
To guide students through calculating the expected value, you can introduce the following formula and explanation steps:
1. **Understand the Concept of Expected Value**:
- The expected value (EV) in this context represents the average payout that the insurance company expects to make, considering both the payout scenario (i.e., the policyholder dies) and the non-payout scenario (i.e., the policyholder survives).
2. **Calculation Method**:
- Given:
- Probability of surviving to age 26, \( P(\text{survive}) = 0.993 \)
- Therefore, probability of not surviving (dying) within the year, \( P(\text{die}) = 1 - 0.993 = 0.007 \)
- Payout amount if the 25-year-old male dies within the year = $16,000
- Cost of the insurance policy = $100
3. **Formula Application**:
- EV can be calculated using the following steps:
- Expected payout if the policyholder dies: \( E(\text{die}) = P(\text{die}) \times \text{Payout amount} = 0.007 \times 16000 \)
- Expected expense if the policyholder survives is zero.
- Expected value of the insurance policy:
\[
E(\text{insurance}) = P(\text{survive}) \times (- \text{Cost} ) + P(\text{die}) \times (\text{Payout} - \text{Cost})
\]
4. **Substitute Numerical Values**:
- Calculation for probability of dying:
\[
0.007 \times 16000 = 112
\]
- Calculation for the expected value:
\[
EV(\text{insurance}) = 0.993 \times (- 100) + 0.007 \times (16000 - 100](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F128593f5-7ea4-4e3b-94cd-55abf91c7165%2Fe9d2db29-f384-4cc2-8b45-e8dca68f80df%2Fb1koffc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Life Insurance Expected Value Calculation
---
#### Problem Statement:
Assume that the probability of a 25-year-old male living to age 26, based on mortality tables, is 0.993. If a 16,000 dollar one-year term life insurance policy on a 25-year-old male costs 100 dollars, what is its expected value?
---
#### Calculation:
**What is the expected value?**
The expected value is \[ ______ \] dollars.
---
To guide students through calculating the expected value, you can introduce the following formula and explanation steps:
1. **Understand the Concept of Expected Value**:
- The expected value (EV) in this context represents the average payout that the insurance company expects to make, considering both the payout scenario (i.e., the policyholder dies) and the non-payout scenario (i.e., the policyholder survives).
2. **Calculation Method**:
- Given:
- Probability of surviving to age 26, \( P(\text{survive}) = 0.993 \)
- Therefore, probability of not surviving (dying) within the year, \( P(\text{die}) = 1 - 0.993 = 0.007 \)
- Payout amount if the 25-year-old male dies within the year = $16,000
- Cost of the insurance policy = $100
3. **Formula Application**:
- EV can be calculated using the following steps:
- Expected payout if the policyholder dies: \( E(\text{die}) = P(\text{die}) \times \text{Payout amount} = 0.007 \times 16000 \)
- Expected expense if the policyholder survives is zero.
- Expected value of the insurance policy:
\[
E(\text{insurance}) = P(\text{survive}) \times (- \text{Cost} ) + P(\text{die}) \times (\text{Payout} - \text{Cost})
\]
4. **Substitute Numerical Values**:
- Calculation for probability of dying:
\[
0.007 \times 16000 = 112
\]
- Calculation for the expected value:
\[
EV(\text{insurance}) = 0.993 \times (- 100) + 0.007 \times (16000 - 100
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