List the sample space for rolling two dice and finding the sum of the numbers. How many 8's are there in the sample space? [Assume that rolling a 3 and a 5 is the same as rolling a 5 and a 3.]
Responses
A 33
B 55
C 22
D 4
The sample space consists of all possible combinations of the numbers rolled on the two dice. We can represent this using a table:
| | 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 |
For example, if we roll a 1 and a 4, the sum is 5.
To count the number of 8's, we simply count the number of pairs of dice that sum to 8. We can see that there are 5 such pairs: (2,6), (3,5), (4,4), (5,3), and (6,2). Therefore, the answer is B) 55.