Suppose that you are offered the following "deal." You roll a six sided die. If you roll a 6, you win $9. If you roll a 4 or 5, you win $3. Otherwise, you pay $6. 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 Table X P(X) b. Find the expected profit. $ c. Interpret the expected value. O If you play many games you will likely lose on average very close to $0.50 per game. You will win this much if you play a game. This is the most likely amount of money you will win. (Round to the nearest cent)
Suppose that you are offered the following "deal." You roll a six sided die. If you roll a 6, you win $9. If you roll a 4 or 5, you win $3. Otherwise, you pay $6. 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 Table X P(X) b. Find the expected profit. $ c. Interpret the expected value. O If you play many games you will likely lose on average very close to $0.50 per game. You will win this much if you play a game. This is the most likely amount of money you will win. (Round to the nearest cent)
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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![### Interactive Probability Exercise
**Scenario:**
You are offered the following deal:
- Roll a six-sided die.
- If you roll a 6, you win $9.
- If you roll a 4 or 5, you win $3.
- Otherwise, you pay $6.
#### Task Breakdown:
a. **Complete the Probability Distribution Table:**
Create a table with the X values (profit) arranged from smallest to largest. Include probabilities (P(X)) rounded to four decimal places.
| X | P(X) |
|-----|-------|
| | |
| | |
| | |
| | |
b. **Calculate the Expected Profit:**
- Find the expected profit and round it to the nearest cent.
- Input the value in the provided field: $ [Text Field]
c. **Interpret the Expected Value:**
- Choose one of the following interpretations:
- If you play many games, you will likely lose on average very close to $0.50 per game.
- You will win this much if you play a game.
- This is the most likely amount of money you will win.
d. **Decision Making:**
- Based on the expected value, decide if you should play this game:
- Yes, since the expected value is positive, you would be very likely to come home with more money if you played many games.
- No, this is a gambling game and it is always a bad idea to gamble.
- Yes, because you can win $9.00 which is greater than the $6.00 that you can lose.
- No, since the expected value is negative, you would be very likely to come home with less money if you played many games.
### Reflection:
Consider probability, expected outcomes, and decision-making in uncertain situations. Use this exercise to analyze risk and reward in probability scenarios.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc614d0cc-0eed-46aa-b3af-63162652eb2c%2F574bfb7c-6cac-4dd4-becd-605039cbba91%2Fud9szr_processed.png&w=3840&q=75)
Transcribed Image Text:### Interactive Probability Exercise
**Scenario:**
You are offered the following deal:
- Roll a six-sided die.
- If you roll a 6, you win $9.
- If you roll a 4 or 5, you win $3.
- Otherwise, you pay $6.
#### Task Breakdown:
a. **Complete the Probability Distribution Table:**
Create a table with the X values (profit) arranged from smallest to largest. Include probabilities (P(X)) rounded to four decimal places.
| X | P(X) |
|-----|-------|
| | |
| | |
| | |
| | |
b. **Calculate the Expected Profit:**
- Find the expected profit and round it to the nearest cent.
- Input the value in the provided field: $ [Text Field]
c. **Interpret the Expected Value:**
- Choose one of the following interpretations:
- If you play many games, you will likely lose on average very close to $0.50 per game.
- You will win this much if you play a game.
- This is the most likely amount of money you will win.
d. **Decision Making:**
- Based on the expected value, decide if you should play this game:
- Yes, since the expected value is positive, you would be very likely to come home with more money if you played many games.
- No, this is a gambling game and it is always a bad idea to gamble.
- Yes, because you can win $9.00 which is greater than the $6.00 that you can lose.
- No, since the expected value is negative, you would be very likely to come home with less money if you played many games.
### Reflection:
Consider probability, expected outcomes, and decision-making in uncertain situations. Use this exercise to analyze risk and reward in probability scenarios.
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