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. In the carnival game Under-or-Over-Seven, a pair of fair dice is rolled once, and the...

. 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, the player can bet $1 that the sum will be under 7—that is, 2, 3, 4, 5, or 6. For this bet, the player wins $1 if the result is under 7 and loses $1 if the outcome equals or is greater than 7. Similarly, the player can bet $1 that the sum will be over 7—that is, 8, 9, 10, 11, or 12. Here, the player wins $1 if the result is over 7 but loses $1 if the result is 7 or under. A third method of play is to bet $1 on the outcome 7. For this bet, the player wins $4 if the result of the roll is 7 and loses $1 otherwise.

(A) Show that the expected long-run profit (or loss) to the player is the same, no matter which method of play is used.

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Answer #1

Solutions . From given information, table is shown in The we can woute below. Die 2 Spiel 1 1 1 2 2 3 3 4 ū 9 10 11 | 7 | 8 |to enter in one stars in online online - M 12 Construct the probability distribution 37e pre senting the different outcomes tequals to or is greater The Than outcome 7 P(x) -1$ +1 $ -2) const duct the probability distribution representing the differeX P(x) H $ *) - (3) contruct the probability distribution ore presenting the different outcomes that are possible for a $i beA show that the expected long-run profit (or loss) to the player is The same, no matter which method of play is used From par

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