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Suppose that you are offered the following "deal." You roll a six sided die. If you roll a 6, you win $8. If you roll a 4 or 5, you win $2. Otherwise, you pay $4. 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 P(X) b. Find the expected profit. S (Round to the nearest cent) c. Interpret the expected value. O You will win this much if you play a game. O This is the most likely amount of money you will win. O f you play many games you will likely break close to even.

Suppose that you are offered the following "deal." You roll a six sided die. If you roll a 6, you win $8. If you roll a 4 or 5, you win $2. Otherwise, you pay $4. 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 P(X) b. Find the expected profit. S (Round to the nearest cent) c. Interpret the expected value. O You will win this much if you play a game. O This is the most likely amount of money you will win. O f you play many games you will likely break close to even.

MATLAB: An Introduction with Applications
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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**Title: Probability and Expected Value Exercise** --- **Scenario:** Suppose that you are offered the following "deal." You roll a six-sided die. If you roll a 6, you win $8. If you roll a 4 or 5, you win $2. Otherwise, you pay $4. **Tasks:** 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. | X | P(X) | |------|--------| | | | | | | | | | b. **Find the expected profit:** $______ (Round to the nearest cent) c. **Interpret the expected value:** - You will win this much if you play a game. - This is the most likely amount of money you will win. - If you play many games you will likely break close to even. d. **Based on the expected value, should you play this game?** - No, this is a gambling game and it is always a bad idea to gamble. - Yes, since the expected value is positive, you would be very likely to come home with more money if you played many games. - No, since the expected value is negative, you would be very likely to come home with less money if you played many games. - Yes, because you can win $8.00 which is greater than the $4.00 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. **Diagram Explanation:** There is a **Probability Distribution Table** with columns for profit values (X) and probabilities (P(X)), meant to be completed based on the given scenario. --- **Considerations for Educators:** This exercise demonstrates the concept of expected value and its implications in decision-making, particularly in the context of probability and gambling. Encourage students to calculate the probabilities and profits to enhance their understanding of mathematical expectations.
Transcribed Image Text:**Title: Probability and Expected Value Exercise** --- **Scenario:** Suppose that you are offered the following "deal." You roll a six-sided die. If you roll a 6, you win $8. If you roll a 4 or 5, you win $2. Otherwise, you pay $4. **Tasks:** 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. | X | P(X) | |------|--------| | | | | | | | | | b. **Find the expected profit:** $______ (Round to the nearest cent) c. **Interpret the expected value:** - You will win this much if you play a game. - This is the most likely amount of money you will win. - If you play many games you will likely break close to even. d. **Based on the expected value, should you play this game?** - No, this is a gambling game and it is always a bad idea to gamble. - Yes, since the expected value is positive, you would be very likely to come home with more money if you played many games. - No, since the expected value is negative, you would be very likely to come home with less money if you played many games. - Yes, because you can win $8.00 which is greater than the $4.00 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. **Diagram Explanation:** There is a **Probability Distribution Table** with columns for profit values (X) and probabilities (P(X)), meant to be completed based on the given scenario. --- **Considerations for Educators:** This exercise demonstrates the concept of expected value and its implications in decision-making, particularly in the context of probability and gambling. Encourage students to calculate the probabilities and profits to enhance their understanding of mathematical expectations.
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