5. A spinner ís numbered rom i to 5 and each number is equaily ikely to come up. A player bets $1.00 on a number and gets $5.00 back if the pointer lands on the number chosen. Otherwise the player loses his $1.00. What is the expected value of the game?
5. A spinner ís numbered rom i to 5 and each number is equaily ikely to come up. A player bets $1.00 on a number and gets $5.00 back if the pointer lands on the number chosen. Otherwise the player loses his $1.00. What is the expected value of the game?
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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My current understanding of this problem is that if the player wins, they receive the five dollars in exchange for the one dollar, ending up with four dollars, but I don't know if they get the dollar back, meaning they'd end up with six dollars. Does this seem correct? Thank you for any help that you can offer!
![**Text Transcription for Educational Website**
**4. Probability of Uninsured Drivers**
In a survey of 100 drivers, the number of uninsured drivers was 23. If you are rear-ended by another driver, what are the odds the other driver is not insured?
- Calculation:
Define odds in favor of uninsured as \( \frac{23}{77} \).
\[
\frac{23}{100} \text{ (Probability of uninsured)}
\]
\[
\frac{77}{100} \text{ (Probability of insured)}
\]
Simplified odds: \(\frac{23}{77}\).
**5. Game Spinner Expected Value Calculation**
A spinner is numbered from 0 to 5 and each number is equally likely to come up. A player bets $1.00 on a number and gets $5.00 back if the pointer lands on the number chosen. Otherwise, the player loses their $1.00. What is the expected value of the game?
- **Calculation**:
\[
E = \frac{1}{6}(5 - 1) + \frac{5}{6}(-1)
\]
\[
= \frac{4}{6} - \frac{5}{6}
\]
\[
= -\frac{1}{6}
\]
\[
E \approx -\$0.17
\]
**Conclusion**: The expected value of the game is approximately -$0.17, indicating a slight expected loss per game.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0ebb7db2-9cc8-4bee-bcd9-bae3e0de13a5%2F24fe340e-8760-4279-b500-eb516495a4fd%2Fhhjjd6k.jpeg&w=3840&q=75)
Transcribed Image Text:**Text Transcription for Educational Website**
**4. Probability of Uninsured Drivers**
In a survey of 100 drivers, the number of uninsured drivers was 23. If you are rear-ended by another driver, what are the odds the other driver is not insured?
- Calculation:
Define odds in favor of uninsured as \( \frac{23}{77} \).
\[
\frac{23}{100} \text{ (Probability of uninsured)}
\]
\[
\frac{77}{100} \text{ (Probability of insured)}
\]
Simplified odds: \(\frac{23}{77}\).
**5. Game Spinner Expected Value Calculation**
A spinner is numbered from 0 to 5 and each number is equally likely to come up. A player bets $1.00 on a number and gets $5.00 back if the pointer lands on the number chosen. Otherwise, the player loses their $1.00. What is the expected value of the game?
- **Calculation**:
\[
E = \frac{1}{6}(5 - 1) + \frac{5}{6}(-1)
\]
\[
= \frac{4}{6} - \frac{5}{6}
\]
\[
= -\frac{1}{6}
\]
\[
E \approx -\$0.17
\]
**Conclusion**: The expected value of the game is approximately -$0.17, indicating a slight expected loss per game.
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