2 You need to borrow money for gas, so you ask your mother. Before giving you money, she makes You play a game. She wants you to spin a spinner That has bevenly divided wedges. Three red, two one blue. She will give 17 2 if you land geen on ved, 08 it You land on green, and II it You land on blue. and a Determine the expected value of the game- B How much you expect to win if you play this Game 25 time?
2 You need to borrow money for gas, so you ask your mother. Before giving you money, she makes You play a game. She wants you to spin a spinner That has bevenly divided wedges. Three red, two one blue. She will give 17 2 if you land geen on ved, 08 it You land on green, and II it You land on blue. and a Determine the expected value of the game- B How much you expect to win if you play this Game 25 time?
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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![### Probability and Expected Value
#### Scenario:
You need to borrow money for gas, so you ask your mother. Before giving you money, she makes you play a game. She wants you to spin a spinner that has 6 evenly divided wedges: three red, two green, and one blue. She will give you:
- $2 if you land on red
- $8 if you land on green
- $11 if you land on blue
#### Questions:
a. **Determine the expected value of the game.**
b. **How much do you expect to win if you play this game 25 times?**
#### Explanation:
1. **Determine the expected value of the game:**
To find the expected value (EV), you multiply each outcome by its probability and then sum up these values.
- The probability of landing on red: \( P(\text{Red}) = \frac{3}{6} = 0.5 \)
- The probability of landing on green: \( P(\text{Green}) = \frac{2}{6} \approx 0.333 \)
- The probability of landing on blue: \( P(\text{Blue}) = \frac{1}{6} \approx 0.167 \)
Now, calculate the expected value using these probabilities:
\[
\text{EV} = (2 \times 0.5) + (8 \times 0.333) + (11 \times 0.167)
\]
- \(2 \times 0.5 = 1\)
- \(8 \times 0.333 \approx 2.664\)
- \(11 \times 0.167 \approx 1.837\)
\[
\text{EV} = 1 + 2.664 + 1.837 = 5.501
\]
So, the expected value of the game is approximately $5.501.
2. **How much you expect to win if you play this game 25 times?**
To find the total expected win over 25 spins, multiply the expected value by 25:
\[
\text{Total Expected Win} = \text{EV} \times 25
\]
\[
\text{Total Expected Win} = 5.501 \times 25 = 137](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F024320af-d9be-4d7b-8f7d-2aa3a761963b%2F921f189c-2694-4557-a14c-5db31f69b950%2F9g65sf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Probability and Expected Value
#### Scenario:
You need to borrow money for gas, so you ask your mother. Before giving you money, she makes you play a game. She wants you to spin a spinner that has 6 evenly divided wedges: three red, two green, and one blue. She will give you:
- $2 if you land on red
- $8 if you land on green
- $11 if you land on blue
#### Questions:
a. **Determine the expected value of the game.**
b. **How much do you expect to win if you play this game 25 times?**
#### Explanation:
1. **Determine the expected value of the game:**
To find the expected value (EV), you multiply each outcome by its probability and then sum up these values.
- The probability of landing on red: \( P(\text{Red}) = \frac{3}{6} = 0.5 \)
- The probability of landing on green: \( P(\text{Green}) = \frac{2}{6} \approx 0.333 \)
- The probability of landing on blue: \( P(\text{Blue}) = \frac{1}{6} \approx 0.167 \)
Now, calculate the expected value using these probabilities:
\[
\text{EV} = (2 \times 0.5) + (8 \times 0.333) + (11 \times 0.167)
\]
- \(2 \times 0.5 = 1\)
- \(8 \times 0.333 \approx 2.664\)
- \(11 \times 0.167 \approx 1.837\)
\[
\text{EV} = 1 + 2.664 + 1.837 = 5.501
\]
So, the expected value of the game is approximately $5.501.
2. **How much you expect to win if you play this game 25 times?**
To find the total expected win over 25 spins, multiply the expected value by 25:
\[
\text{Total Expected Win} = \text{EV} \times 25
\]
\[
\text{Total Expected Win} = 5.501 \times 25 = 137
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