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

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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.

i. Construct the probability distribution representing the different outcomes that are possible for a $1 bet on under 7.

ii. Construct the probability distribution representing the different outcomes that are possible for a $1 bet on over 7.

iii. Construct the probability distribution representing the different outcomes that are possible for a $1 bet on 7.

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

Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...
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Basic Business Statistics Concepts And Applications

ISBN: 9780132168380

12th Edition

Authors: Mark L. Berenson, David M. Levine, Timothy C. Krehbiel

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