MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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![### Understanding Expected Value in Probability
Suppose that you are offered the following "deal." You roll a six-sided die. If you roll a 6, you win $6. If you roll a 3, 4, or 5, you win $3. Otherwise, you pay $2.
#### Step-by-Step Approach:
**a. Complete the Probability Distribution Function (PDF) Table**
- List potential profits (X values), from smallest to largest.
- Round to 4 decimal places where appropriate.
| X | P(X) |
|---------|-------------|
| | |
| | |
| | |
| | |
**b. Find the Expected Profit**
- Calculate and input the value, rounding to the nearest cent.
\[ \text{Expected Profit: } \$ \_\_\_\_ \]
**c. Interpret the Expected Value**
- Options to interpret the expected value:
- If you play many games, on average, you will likely win or lose (if negative) this amount.
- You will win this much if you play a game.
- This is the most likely amount of money you will win.
**d. Should You Play This Game?**
- Determine based on calculated expected value:
- No, this is gambling and it's always bad to gamble.
- No, with a negative expected value, you’re likely to lose money over many games.
- Yes, a positive expected value indicates more likely gains over many games.
- Yes, a $6 win is greater than the $2 loss.
- Yes, with an expected value of 0, you’ll break even over many games, making it risk-free fun.
**Graphs and Diagrams:**
- **Probability Distribution Table**:
The table should include values for X, representing different profit/loss outcomes, and corresponding probabilities for each outcome, P(X).
Understanding this concept helps in making informed decisions in probability-based scenarios, commonly encountered in both academic studies and real-world applications such as gambling.](https://content.bartleby.com/qna-images/question/11f84057-ddc6-4a16-833f-eeebb801b1ce/951b6a0a-516e-48e4-b3c0-290de1047e65/xfhtcjs_processed.png)
Transcribed Image Text:### Understanding Expected Value in Probability
Suppose that you are offered the following "deal." You roll a six-sided die. If you roll a 6, you win $6. If you roll a 3, 4, or 5, you win $3. Otherwise, you pay $2.
#### Step-by-Step Approach:
**a. Complete the Probability Distribution Function (PDF) Table**
- List potential profits (X values), from smallest to largest.
- Round to 4 decimal places where appropriate.
| X | P(X) |
|---------|-------------|
| | |
| | |
| | |
| | |
**b. Find the Expected Profit**
- Calculate and input the value, rounding to the nearest cent.
\[ \text{Expected Profit: } \$ \_\_\_\_ \]
**c. Interpret the Expected Value**
- Options to interpret the expected value:
- If you play many games, on average, you will likely win or lose (if negative) this amount.
- You will win this much if you play a game.
- This is the most likely amount of money you will win.
**d. Should You Play This Game?**
- Determine based on calculated expected value:
- No, this is gambling and it's always bad to gamble.
- No, with a negative expected value, you’re likely to lose money over many games.
- Yes, a positive expected value indicates more likely gains over many games.
- Yes, a $6 win is greater than the $2 loss.
- Yes, with an expected value of 0, you’ll break even over many games, making it risk-free fun.
**Graphs and Diagrams:**
- **Probability Distribution Table**:
The table should include values for X, representing different profit/loss outcomes, and corresponding probabilities for each outcome, P(X).
Understanding this concept helps in making informed decisions in probability-based scenarios, commonly encountered in both academic studies and real-world applications such as gambling.
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