The player pays a fee of $5 to play. The player then rolls a 12-sided die three times. If the player rolls a 7 on any of the three rolls, they win a prize. The prize is determined by the number of 7s rolled. If the player rolls one 7, they win $5. If the player rolls two 7s, they win a $10. If the player rolls three 7s, they win $20. Compare the theoretical results of the game to the experimental results, including a discussion of whether the results were typical or rare. Theoretical results: Roll (including all 3 rolls) Result Money earned 1 7,7,7 $15 2 2,4,5 $5 3 5,7,9 $5 4 1,9,3 $0 5 2,12,7 $5 6 3,12,3 $0 7 7,4,8 $5 8 6,7,7 $10 9 5,12,4 $0 10 7,5,7 $10 Experimental results: Roll (including all 3 rolls) Result Money earned 1 1,3,7 $5 2 3,6,4 $0 3 7,6,9 $5 4 8,7,7 $10 5 11,4,1 $0 6 6,5,7 $7 7 4,6,3 $0 8 7,1,9 $7 9 4,4,3 $0 10 5,6,7 $7
The player pays a fee of $5 to play. The player then rolls a 12-sided die three times. If the player rolls a 7 on any of the three rolls, they win a prize. The prize is determined by the number of 7s rolled. If the player rolls one 7, they win $5. If the player rolls two 7s, they win a $10. If the player rolls three 7s, they win $20.
Compare the theoretical results of the game to the experimental results, including a discussion of whether the results were typical or rare.
Theoretical results:
|
Roll (including all 3 rolls) |
Result |
Money earned |
|
1 |
7,7,7 |
$15 |
|
2 |
2,4,5 |
$5 |
|
3 |
5,7,9 |
$5 |
|
4 |
1,9,3 |
$0 |
|
5 |
2,12,7 |
$5 |
|
6 |
3,12,3 |
$0 |
|
7 |
7,4,8 |
$5 |
|
8 |
6,7,7 |
$10 |
|
9 |
5,12,4 |
$0 |
|
10 |
7,5,7 |
$10 |
Experimental results:
|
Roll (including all 3 rolls) |
Result |
Money earned |
|
1 |
1,3,7 |
$5 |
|
2 |
3,6,4 |
$0 |
|
3 |
7,6,9 |
$5 |
|
4 |
8,7,7 |
$10 |
|
5 |
11,4,1 |
$0 |
|
6 |
6,5,7 |
$7 |
|
7 |
4,6,3 |
$0 |
|
8 |
7,1,9 |
$7 |
|
9 |
4,4,3 |
$0 |
|
10 |
5,6,7 |
$7 |
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