Question

After rolling a pair of fair, six-sided dice, what is the probability that the sum of the outcomes is at least 4 but less than 12?

(Round your answer to the third decimal place)

Answer 1

The two dice are assumed distinct.
How many ways are there to get the desired outcomes (success):
Sum
4 1-3,2-2,3-1 so 3
5 1-4,2-3,3,2,4,1 so 4
6 1-5,2-4,3-3,4-2,5-1 so 5
7 1-6,2-5,3-4,4-3,5-2,6-1 so 6
...
Continue until 11 (less than 12) and add the total number of ways to get success.
The number of possible outcomes (Ω) is 6×6=36.
Divide the number of successful outcomes by the number of possible outcomes to get the probability of success.