In the carnival game Under-or-Over-Seven, a pair of fair dice is rolled once, and the resulting...
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 $2.00 that the sum will be under 7, that is, 2, 3, 4, 5, or 6. For this bet, the player wins $2.00 if the result is under 7 and loses $2.00 if the outcome equals or is greater than 7. Similarly, using method two, the player can bet $2.00 that the sum will be over 7, that is, 8, 9, 10, 11, or 12. Here, the player wins $2.00 if the result is over 7 but loses $2.00 if the result is 7 or under. A third method of play is to bet $2.00 on the outcome 7. For this bet, the player wins $8.00 if the result of the roll is 7 and loses $2.00 otherwise. Complete parts (a) through (d).
|
Outcomes of a two dice roll |
|
1 |
2 |
3 |
4 |
5 |
6 |
|
|
1 |
2 |
3 |
4 |
5 |
6 |
7 |
|
2 |
3 |
4 |
5 |
6 |
7 |
8 |
|
3 |
4 |
5 |
6 |
7 |
8 |
9 |
|
4 |
5 |
6 |
7 |
8 |
9 |
10 |
|
5 |
6 |
7 |
8 |
9 |
10 |
11 |
|
6 |
7 |
8 |
9 |
10 |
11 |
12 |
a. Construct the probability distribution representing the different outcomes that are possible for a $1.00 bet using method one.
|
X |
P(X) |
|---|---|
|
$ |
type a fraction |
|
−$ |
fraction |
(Type an exact answer in simplified form.)
b. Construct the probability distribution representing the different outcomes that are possible for a $1.00 bet using method two.
|
X |
P(X) |
|---|---|
|
$ |
fraction |
|
−$ |
fraction |
(Type an exact answer in simplified form.)
c. Construct the probability distribution representing the different outcomes that are possible for a $1.00 bet using method three.
|
X |
P(X) |
|---|---|
|
$ |
|
|
−$ |
d. What is the expected long-run profit (or loss) to the player for each of the three methods of play?
|
Method one expected profit (or loss) |
muμ |
= |
$ |
|
Method two expected profit (or loss) |
muμ |
= |
$ |
|
Method three expected profit (or loss) |
muμ |
= |
$ |
|
$(Round to the nearest cent as needed.) |
Homework Answers
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In the carnival game Under-or-Over-Seven, a pair of fair dice
is rolled once, and the resulting...
the carnival game Under-or-Over-Seven, a pair of fair dice is rolled once, and the resulting sum...
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...
. In the carnival game Under-or-Over-Seven, a pair of fair dice is rolled once, and the...
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