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six, you you roll a one, two, or three, you pay $6. O Part (a) What are you ultimately interested in here (the value of the roll or the money you win)? O the amount of winnings the number rolled the number of times a six is rolled O the type of die O Part (b) In words, define the Random Variable X. O 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 O Part (c) List the values that X may take on. O $5, $6, $10 O 4, 5, 6 O -S6, $5, $10 O 1, 2, 3, 4, 5, 6

six, you you roll a one, two, or three, you pay $6. O Part (a) What are you ultimately interested in here (the value of the roll or the money you win)? O the amount of winnings the number rolled the number of times a six is rolled O the type of die O Part (b) In words, define the Random Variable X. O 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 O Part (c) List the values that X may take on. O $5, $6, $10 O 4, 5, 6 O -S6, $5, $10 O 1, 2, 3, 4, 5, 6

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.6: Permutations And Combinations
Problem 70E
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Suppose that you are offered the following "deal." You roll a die. If you roll a six, you win $10. If you roll a four or five, you win $5. If you roll a one, two, or three, you pay $6. O Part (a) What are you ultimately interested in here (the value of the roll or the money you win)? the amount of winnings the number rolled the number of times a six is rolled O the type of die O 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 O Part (c) List the values that X may take on. $5, $6, $10 4. 5. 6 O -$6, $5, $10 O 1, 2, 3, 4, 5, 6 O 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.) P(X = x) x · P(X = x) 6 4 or 5 1, 2, or 3 O 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.) $ O Part (f) Based on numerical values, should you take the deal? Yes, you should take the deal because the expected value is positive. O No, you should not take the deal because the expected value is negative.
Transcribed Image Text:Suppose that you are offered the following "deal." You roll a die. If you roll a six, you win $10. If you roll a four or five, you win $5. If you roll a one, two, or three, you pay $6. O Part (a) What are you ultimately interested in here (the value of the roll or the money you win)? the amount of winnings the number rolled the number of times a six is rolled O the type of die O 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 O Part (c) List the values that X may take on. $5, $6, $10 4. 5. 6 O -$6, $5, $10 O 1, 2, 3, 4, 5, 6 O 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.) P(X = x) x · P(X = x) 6 4 or 5 1, 2, or 3 O 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.) $ O Part (f) Based on numerical values, should you take the deal? Yes, you should take the deal because the expected value is positive. O No, you should not take the deal because the expected value is negative.
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