2. You are allowed to play a game with the following rules. You pay $1 to flip a fair Quarter, Nickel and Dime. If they all three come up Heads or all three come up Tails you get $3. You are allowed to play this as many times as you want. A. Create a Table to goes through the Probabilities for the outcomes (win or lose) B. What is the Expected Value of playing this game? C. Should you play this game?
2. You are allowed to play a game with the following rules. You pay $1 to flip a fair Quarter, Nickel and Dime. If they all three come up Heads or all three come up Tails you get $3. You are allowed to play this as many times as you want. A. Create a Table to goes through the Probabilities for the outcomes (win or lose) B. What is the Expected Value of playing this game? C. Should 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
Related questions
Question
![**Game Rules and Analysis**
You are allowed to play a game with the following rules. You pay $1 to flip a fair Quarter, Nickel, and Dime. If they all three come up Heads or all three come up Tails, you get $3. You are allowed to play this as many times as you want.
**Tasks:**
A. Create a Table to go through the Probabilities for the outcomes (win or lose).
B. What is the Expected Value of playing this game?
C. Should you play this game?
---
**Explanation for Educational Website:**
**Potential Outcomes:**
1. All coins come up Heads.
2. All coins come up Tails.
3. Mixed results (not all Heads or all Tails: any combination of Heads and Tails in different orders).
**Probabilities:**
- Probability of all Heads (HHH) = \( \frac{1}{8} \)
- Probability of all Tails (TTT) = \( \frac{1}{8} \)
- Probability of Mixed results = \(1 - \left(\frac{1}{8} + \frac{1}{8}\right) = \frac{6}{8}\) or \( \frac{3}{4} \)
**Win/Loss Table:**
| Outcome | Probability | Winnings | Net Gain/Loss |
|-----------|-------------|----------|---------------|
| All Heads or All Tails | \( \frac{2}{8} \) or \( \frac{1}{4} \) | $3 | $2 |
| Mixed Results | \( \frac{6}{8} \) or \( \frac{3}{4} \) | $0 | -$1 |
**Expected Value Calculation:**
\[ \text{Expected Value} = \left(\frac{1}{4} \times 2\right) + \left(\frac{3}{4} \times (-1)\right) \]
\[ = \frac{1}{2} - \frac{3}{4} \]
\[ = -\frac{1}{4} \]
The expected value of playing this game is \(-\frac{1}{4}\), meaning you are expected to lose 25 cents per game on average.
**Conclusion:**
Considering the negative expected value, it is not advisable to play this game if you aim to make a profit](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb60b9619-24ed-498e-913b-12564ee6fa56%2F4258cfaa-382a-4236-9376-8e63059a430d%2Fhtoxzxx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Game Rules and Analysis**
You are allowed to play a game with the following rules. You pay $1 to flip a fair Quarter, Nickel, and Dime. If they all three come up Heads or all three come up Tails, you get $3. You are allowed to play this as many times as you want.
**Tasks:**
A. Create a Table to go through the Probabilities for the outcomes (win or lose).
B. What is the Expected Value of playing this game?
C. Should you play this game?
---
**Explanation for Educational Website:**
**Potential Outcomes:**
1. All coins come up Heads.
2. All coins come up Tails.
3. Mixed results (not all Heads or all Tails: any combination of Heads and Tails in different orders).
**Probabilities:**
- Probability of all Heads (HHH) = \( \frac{1}{8} \)
- Probability of all Tails (TTT) = \( \frac{1}{8} \)
- Probability of Mixed results = \(1 - \left(\frac{1}{8} + \frac{1}{8}\right) = \frac{6}{8}\) or \( \frac{3}{4} \)
**Win/Loss Table:**
| Outcome | Probability | Winnings | Net Gain/Loss |
|-----------|-------------|----------|---------------|
| All Heads or All Tails | \( \frac{2}{8} \) or \( \frac{1}{4} \) | $3 | $2 |
| Mixed Results | \( \frac{6}{8} \) or \( \frac{3}{4} \) | $0 | -$1 |
**Expected Value Calculation:**
\[ \text{Expected Value} = \left(\frac{1}{4} \times 2\right) + \left(\frac{3}{4} \times (-1)\right) \]
\[ = \frac{1}{2} - \frac{3}{4} \]
\[ = -\frac{1}{4} \]
The expected value of playing this game is \(-\frac{1}{4}\), meaning you are expected to lose 25 cents per game on average.
**Conclusion:**
Considering the negative expected value, it is not advisable to play this game if you aim to make a profit
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