12. According to Bristol Mutual Life Insurance's mortality table, the probability that a 20-year-old woman will survive 1 year is 0.994 and the probability that she will die within 1 year is 0.006. If a 20- year-old woman buys a $10,000 1-year policy for $100, what is Bristol Mutual's expected gain or loss? The expected value is:
12. According to Bristol Mutual Life Insurance's mortality table, the probability that a 20-year-old woman will survive 1 year is 0.994 and the probability that she will die within 1 year is 0.006. If a 20- year-old woman buys a $10,000 1-year policy for $100, what is Bristol Mutual's expected gain or loss? The expected value is:
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![**Problem 12: Understanding Expected Value in Life Insurance**
According to Bristol Mutual Life Insurance's mortality table, the probability that a 20-year-old woman will survive 1 year is 0.994, and the probability that she will die within 1 year is 0.006. If a 20-year-old woman buys a $10,000 1-year policy for $100, what is Bristol Mutual's expected gain or loss?
The expected value is: __________.
---
To solve this problem, we calculate the expected value by considering two scenarios:
1. **Survival:**
Probability = 0.994
Gain for the insurance company = $100 (since no payout occurs)
2. **Death:**
Probability = 0.006
Loss for the insurance company = $10,000 - $100 = $9,900 (after receiving the policy cost)
**Expected Value Calculation:**
\[ \text{Expected Gain or Loss} = (0.994 \times 100) + (0.006 \times -9900) \]
This equation will give us the expected monetary outcome for the insurance company when a 20-year-old woman buys this policy.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb987d8c1-664b-448b-b573-1ab7f66094f6%2F268e438b-bf44-4598-9c80-e028d3e1db85%2Fxycbym6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 12: Understanding Expected Value in Life Insurance**
According to Bristol Mutual Life Insurance's mortality table, the probability that a 20-year-old woman will survive 1 year is 0.994, and the probability that she will die within 1 year is 0.006. If a 20-year-old woman buys a $10,000 1-year policy for $100, what is Bristol Mutual's expected gain or loss?
The expected value is: __________.
---
To solve this problem, we calculate the expected value by considering two scenarios:
1. **Survival:**
Probability = 0.994
Gain for the insurance company = $100 (since no payout occurs)
2. **Death:**
Probability = 0.006
Loss for the insurance company = $10,000 - $100 = $9,900 (after receiving the policy cost)
**Expected Value Calculation:**
\[ \text{Expected Gain or Loss} = (0.994 \times 100) + (0.006 \times -9900) \]
This equation will give us the expected monetary outcome for the insurance company when a 20-year-old woman buys this policy.
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