Suppose that you are offered the following "deal." You roll a die. If you roll a six, you win $12. If you roll a four or five, you win $5. If you roll a one, two, or three, you pay $4. - Part (a) What are you ultimately interested in here (the value of the roll or the money you win)? O the number rolled the amount of winnings O the type of die O the number of times a six is rolled Part (b) In words, define the Random Variable X. ○ the amount of winnings the probability of rolling a four ○ the amount of money made by rolling a six O the amount of numbers that can be rolled - Part (c) List the values that X may take on. 4,5,6 ○ 1, 2, 3, 4, 5, 6 ○ -$4, $5, $12 ○ $4, $5, $12 Part (d) Construct a PDF. (Enter your answers for P(X = x) as fractions. Round your answers for x · P(X = x) to two decimal places.) 6 4 or 5 1, 2, or 3 X P(X = x) x. P(X = x) Part (e) Over the long run of playing this game, what are your expected average winnings per game? (Round your answer to two decimal places.) $ Part (f) Based on numerical values, should you take the deal? ◇ Yes, you should take the deal because the expected value is positive. No, you should not take the deal because the expected value is negative.

Suppose that you are offered the following "deal." You roll a die. If you roll a six, you win $12. If you roll a four or five, you win $5. If you roll a one, two, or three, you pay $4. - Part (a) What are you ultimately interested in here (the value of the roll or the money you win)? O the number rolled the amount of winnings O the type of die O the number of times a six is rolled Part (b) In words, define the Random Variable X. ○ the amount of winnings the probability of rolling a four ○ the amount of money made by rolling a six O the amount of numbers that can be rolled - Part (c) List the values that X may take on. 4,5,6 ○ 1, 2, 3, 4, 5, 6 ○ -$4, $5, $12 ○ $4, $5, $12 Part (d) Construct a PDF. (Enter your answers for P(X = x) as fractions. Round your answers for x · P(X = x) to two decimal places.) 6 4 or 5 1, 2, or 3 X P(X = x) x. P(X = x) Part (e) Over the long run of playing this game, what are your expected average winnings per game? (Round your answer to two decimal places.) $ Part (f) Based on numerical values, should you take the deal? ◇ Yes, you should take the deal because the expected value is positive. No, you should not take the deal because the expected value is negative.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

ChapterP: Prologue: Calculator Arithmetic

Section: Chapter Questions

Problem 29E: The Advantage Cash Card At the student union on a certain campus, you can save on food purchases by...

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The Advantage Cash Card At the student union on a certain campus, you can save on food purchases by using the Advantage Cash Card. You deposit money into an Advantage Cash account and are issued a credit card the you use to purchase food. The card has several advantages: If you open your Advantage Cash account for 200 or more, a 5% bonus is added to your account balance. When you use your Advantage Cash Card, you receive 5% off the retail price of any food purchase. When you buy food with cash, you must pay a sales tax of 7.375%. With the Advantage Cash Card, you pay no sales tax. a.An item retails for 1.00. What do you pay if you use your Advantage Cash Card? b.An item retails for 1.00. What do you pay if you use cash? Round your answer to five decimal places for use in part d. c.What retail value of food will you be able to purchase if you open an Advantage Cash account for 300? Suggestion: Dont forget your 5% bonus and use the results of part a d.What retail value of food would you be able to purchase with 300 if you spend it as cash at the food court? Suggestion: Use the results of part b e.Calculate the percentage increase from your answer for part d to your answer for part c. Explain in practical terms the meaning of this percentage.