### Understanding Probability and Expected Value#### ScenarioYou are offered the following "deal." You roll a six-sided die:- If you roll a 6, you win $7.- If you roll a 3, 4, or 5, you win $2.- Otherwise, you pay $3.#### Tasks##### a. Complete the Probability Distribution Function (PDF) TableFill in the X values, where X is the profit, listed from smallest to largest. Round to 4 decimal places.| X | P(X) ||-----|------|| | || | || | |##### b. Find the Expected ProfitCalculate the expected profit and round to the nearest cent. **Expected Profit: $________**##### c. Interpret the Expected ValueChoose the interpretation that best describes the expected value:- ☐ This is the most likely amount of money you will win.- ☐ You will win this much if you play a game.- ☐ If you play many games, you will likely win on average very close to $1.17 per game.##### d. Decision Making Based on the Expected ValueBased on the expected value, should you play this game?- ☐ 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.- ☐ Yes, since the expected value is positive, you would be very likely to come home with more money if you played many games.- ☐ Yes, because you can win $7.00 which is greater than the $3.00 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.### Visual ExplanationThe task involves understanding probability distribution and expected values by analyzing scenarios involving a die roll, with a focus on making informed decisions based on calculated risks.

Name: ### Understanding Probability and Expected Value#### ScenarioYou are
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Description: ### Understanding Probability and Expected Value#### ScenarioYou are offered the following "deal." You roll a six-sided die:- If you roll a 6, you win $7.- If you roll a 3, 4, or 5, you win $2.- Otherwise, you pay $3.#### Tasks##### a. Complete the

a. When a die is rolled the possible outcomes are 1,2,3,4,5,6. The probability of obtaining each…

Math

Statistics

Suppose that you are offered the following "deal." You roll a six sided die. If you roll a 6, you win $7. If you roll a 3, 4 or 5, you win $2. Otherwise, you pay $3. 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) p. Find the expected profit. $ (Round to the nearest cent) . Interpret the expected value. O This is the most likely amount of money you will win. O You will win this much if you play a game. O If you play many games you will likely win on average very close to $1.17 per game. d. Based on the expected value, should you play this game? O 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. 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 $7.00 which is greater than the $3.00 that you can lose. O No, since the expected value is negative, you would be very likely to come home with less money if you played many games.

Suppose that you are offered the following "deal." You roll a six sided die. If you roll a 6, you win $7. If you roll a 3, 4 or 5, you win $2. Otherwise, you pay $3. 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) p. Find the expected profit. $ (Round to the nearest cent) . Interpret the expected value. O This is the most likely amount of money you will win. O You will win this much if you play a game. O If you play many games you will likely win on average very close to $1.17 per game. d. Based on the expected value, should you play this game? O 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. 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 $7.00 which is greater than the $3.00 that you can lose. O No, since the expected value is negative, you would be very likely to come home with less money if you played many games.

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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