A bag contains 2 gold marbles, 6 silver marbles, and 23 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $3. If it is silver, you win S2. If it is black, you lose $1. What is your expected value if you play this game?
A bag contains 2 gold marbles, 6 silver marbles, and 23 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $3. If it is silver, you win S2. If it is black, you lose $1. What is your expected value if you play this game?
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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![A bag contains 2 gold marbles, 6 silver marbles, and 23 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $3. If it is silver, you win $2. If it is black, you lose $1.
What is your expected value if you play this game?
$\_\_\_\_
[Submit Question]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1d78f8e5-d6bc-4994-a72a-31391ccd8d53%2Fef81bd57-8cfa-4858-8fbf-32b3b6f511e7%2Feig9dsm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A bag contains 2 gold marbles, 6 silver marbles, and 23 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $3. If it is silver, you win $2. If it is black, you lose $1.
What is your expected value if you play this game?
$\_\_\_\_
[Submit Question]
![**Question 12**
A bag contains 2 gold marbles, 6 silver marbles, and 23 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $3. If it is silver, you win $2. If it is black, you lose $1.
What is your expected value if you play this game?
\[ \text{\$} \_\_ \]
[Submit Question Button]
---
**Explanation for Educational Purposes:**
To calculate the expected value of this game, follow these steps:
1. **Determine the Total Number of Marbles:**
\[
2 \text{ (gold)} + 6 \text{ (silver)} + 23 \text{ (black)} = 31 \text{ marbles in total}
\]
2. **Calculate the Probability of Each Marble:**
- Probability of drawing a gold marble: \( \frac{2}{31} \)
- Probability of drawing a silver marble: \( \frac{6}{31} \)
- Probability of drawing a black marble: \( \frac{23}{31} \)
3. **Determine the Expected Value:**
Use the formula for expected value:
\[
EV = (\text{Probability of Gold} \times \text{Value of Gold}) + (\text{Probability of Silver} \times \text{Value of Silver}) + (\text{Probability of Black} \times \text{Value of Black})
\]
\[
EV = \left(\frac{2}{31} \times 3\right) + \left(\frac{6}{31} \times 2\right) + \left(\frac{23}{31} \times -1\right)
\]
4. **Calculate the Expected Value:**
- Contribution from gold marbles: \(\frac{2}{31} \times 3 = \frac{6}{31}\)
- Contribution from silver marbles: \(\frac{6}{31} \times 2 = \frac{12}{31}\)
- Contribution from black marbles: \(\frac{23}{31} \times -1 = -\frac{23}{31}\)
\[
EV = \frac{6}{31} + \frac{12}{31} -](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1d78f8e5-d6bc-4994-a72a-31391ccd8d53%2Fef81bd57-8cfa-4858-8fbf-32b3b6f511e7%2F6ogko5w_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 12**
A bag contains 2 gold marbles, 6 silver marbles, and 23 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $3. If it is silver, you win $2. If it is black, you lose $1.
What is your expected value if you play this game?
\[ \text{\$} \_\_ \]
[Submit Question Button]
---
**Explanation for Educational Purposes:**
To calculate the expected value of this game, follow these steps:
1. **Determine the Total Number of Marbles:**
\[
2 \text{ (gold)} + 6 \text{ (silver)} + 23 \text{ (black)} = 31 \text{ marbles in total}
\]
2. **Calculate the Probability of Each Marble:**
- Probability of drawing a gold marble: \( \frac{2}{31} \)
- Probability of drawing a silver marble: \( \frac{6}{31} \)
- Probability of drawing a black marble: \( \frac{23}{31} \)
3. **Determine the Expected Value:**
Use the formula for expected value:
\[
EV = (\text{Probability of Gold} \times \text{Value of Gold}) + (\text{Probability of Silver} \times \text{Value of Silver}) + (\text{Probability of Black} \times \text{Value of Black})
\]
\[
EV = \left(\frac{2}{31} \times 3\right) + \left(\frac{6}{31} \times 2\right) + \left(\frac{23}{31} \times -1\right)
\]
4. **Calculate the Expected Value:**
- Contribution from gold marbles: \(\frac{2}{31} \times 3 = \frac{6}{31}\)
- Contribution from silver marbles: \(\frac{6}{31} \times 2 = \frac{12}{31}\)
- Contribution from black marbles: \(\frac{23}{31} \times -1 = -\frac{23}{31}\)
\[
EV = \frac{6}{31} + \frac{12}{31} -
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