What is the sample space of the sum of two 6-sided dice where the first number is less than 4? List your values from smallest to largest.
The sample space of the sum of two 6-sided dice where the first number is less than 4 includes the possible sums when the first dice shows a 1, 2, or 3.
When the first dice shows a 1:
- (1,1) = 2
- (1,2) = 3
- (1,3) = 4
- (1,4) = 5
- (1,5) = 6
- (1,6) = 7
When the first dice shows a 2:
- (2,1) = 3
- (2,2) = 4
- (2,3) = 5
- (2,4) = 6
- (2,5) = 7
- (2,6) = 8
When the first dice shows a 3:
- (3,1) = 4
- (3,2) = 5
- (3,3) = 6
- (3,4) = 7
- (3,5) = 8
- (3,6) = 9
Arranging the sums from smallest to largest:
2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9