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. a. Complete the PDF Table. List the X values, where X is the profit, from smallest to largest. Round to 4 decimal places where appropriate. Probability Distribution X P(X) Table b. Find the expected profit. S c. Interpret the expected value. O If you play many games, on average, you will likely win, or lose if negative, close to this amount. O You will win this much if you play a game. O This is the most likely amount of money you will win. (Round to the nearest cent) d. Based on the expected value, should you play this game? O No, this is a gambling game and it is always a bad idea to gamble. O No, since the expected value is negative, you would be very likely to come home with less money if you played many games. O Yes, since the expected value is positive, you would be very likely to come home with more money if you played many games. O Yes, because you can win $6.00 which is greater than the $2.00 that you can lose. Yes, since the expected value is 0, you would be very likely to come very close to breaking even if you played many games, so you might as well have fun at no cost.
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. a. Complete the PDF Table. List the X values, where X is the profit, from smallest to largest. Round to 4 decimal places where appropriate. Probability Distribution X P(X) Table b. Find the expected profit. S c. Interpret the expected value. O If you play many games, on average, you will likely win, or lose if negative, close to this amount. O You will win this much if you play a game. O This is the most likely amount of money you will win. (Round to the nearest cent) d. Based on the expected value, should you play this game? O No, this is a gambling game and it is always a bad idea to gamble. O No, since the expected value is negative, you would be very likely to come home with less money if you played many games. O Yes, since the expected value is positive, you would be very likely to come home with more money if you played many games. O Yes, because you can win $6.00 which is greater than the $2.00 that you can lose. Yes, since the expected value is 0, you would be very likely to come very close to breaking even if you played many games, so you might as well have fun at no cost.
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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![### 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11f84057-ddc6-4a16-833f-eeebb801b1ce%2F951b6a0a-516e-48e4-b3c0-290de1047e65%2Fxfhtcjs_processed.png&w=3840&q=75)
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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