Question

Two dice, one red and one white are rolled. What is the probability that the white die turns up a smaller number than the red dice ?

Answer 1

The sample space has 36 possible combinations of numbers. These can be set out in column form as follows:
6,6 5,6 4,6 3,6 2,6 1,6
6,5 5,5 4,5 3,5 2,5 1,5
6,4 5,4 4,4 3,4 2,4 1,4
6,3 5,3 4,3 3,3 2,3 1,3
6,2 5,2 4,2 3,2 2,2 1,2
6,1 5,1 4,1 3,1 2,1 1,1
Let the left hand number in each pair be the number on the white die. Now count the number of pairs where the left hand number is smaller than the right hand number. Then divide this number by 36 to find the required probability.