In the carnival game Under-or-Over-Seven, a pair of fair dice is rolled once, and the resulting sum determines whether the player wins or loses his or her bet. For example, using method one, the player can bet $4.00 that the sum will be under 7, that is, 2, 3, 4, 5, or 6. For this bet, the player wins $4.00 if the result is under 7 and loses $4.00 if the outcome equals or is greater than 7. Similarly, using method two, the player can bet $4.00 that the sum will be over 7, that is, 8, 9, 10, 11, or 12. Here, the player wins $4.00 if the result is over 7 but loses $4.00 if the result is 7 or under. A third method of play is to bet $4.00 on the outcome 7. For this bet, the player wins $16.00 if the result of the roll is 7 and loses $4.00 otherwise. Table of outcomes is given. A.)Construct the probability distribution representing the different outcomes that are possible for a $4.00 bet using method one. B.)Construct the probability distribution representing the different outcomes that are possible for a $4.00 bet using method two. C.)Construct the probability distribution representing the different outcomes that are possible for a $4.00 bet using method three.
In the carnival game Under-or-Over-Seven, a pair of fair dice is rolled once, and the resulting sum determines whether the player wins or loses his or her bet. For example, using method one, the player can bet $4.00 that the sum will be under 7, that is, 2, 3, 4, 5, or 6. For this bet, the player wins $4.00 if the result is under 7 and loses $4.00 if the outcome equals or is greater than 7. Similarly, using method two, the player can bet $4.00 that the sum will be over 7, that is, 8, 9, 10, 11, or 12. Here, the player wins $4.00 if the result is over 7 but loses $4.00 if the result is 7 or under. A third method of play is to bet $4.00 on the outcome 7. For this bet, the player wins $16.00 if the result of the roll is 7 and loses $4.00 otherwise. Table of outcomes is given.
A.)Construct the probability distribution representing the different outcomes that are possible for a $4.00 bet using method one.
B.)Construct the probability distribution representing the different outcomes that are possible for a $4.00 bet using method two.
C.)Construct the probability distribution representing the different outcomes that are possible for a $4.00 bet using method three.
D.) What is the expected long-run profit (or loss) to the player for each of the three methods of play? (Rounded to nearest cent).
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