Final answer:
The probability of rolling a sum less than 9 with two dice is 25 out of the 36 possible combinations, which simplifies to approximately 69.44%.
Step-by-step explanation:
To calculate the probability of rolling two dice and getting a sum less than 9, we need to first consider all the possible combinations of two six-sided dice. There are a total of 36 combinations since each die has 6 faces. We then count all the combinations that result in a sum less than 9. These combinations are:
- (1,1), (1,2), (1,3), (1,4), (1,5), (1,6)
- (2,1), (2,2), (2,3), (2,4), (2,5), (2,6)
- (3,1), (3,2), (3,3), (3,4), (3,5)
- (4,1), (4,2), (4,3), (4,4), (4,5)
- (5,1), (5,2), (5,3), (5,4)
- (6,1), (6,2), (6,3)
There are 25 combinations where the sum is less than 9. Thus, the probability of getting a sum less than 9 is:
P(sum < 9) = Number of favorable outcomes / Total possible outcomes
= 25 / 36
This simplifies to approximately 0.6944, or 69.44% chance when rolling two dice that the sum will be less than 9.