Question

48. 2 dice are rolled, one black and one white.

How many rolls occur in which the value on the white die is greater than the value on the black die?

Answer 1

2 dice are rolled: one black and one white

Now the total possibilities are 36 as shown below.

(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),(3,6).
(4,1),(4,2),(4,3),(4,4),(4,5),(4,6).
(5,1),(5,2),(5,3),(5,4),(5,5),(5,6).
(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)

In the values (i,j), let i be the outcome from white die and j be the outcome from black die.

We need to find the cases in which i>j

• There are 6 cases in which the outcomes are same (i=j).
• Remaining 30 cases have equal distribution. In half of them i>j and in other half j>i. So the answer would be 15

We can also see the cases in which i>j

(2,1)
(3,1),(3,2)
(4,1),(4,2),(4,3)
(5,1),(5,2),(5,3),(5,4)
(6,1),(6,2),(6,3),(6,4)(6,5)

So, these are the 15 cases in which i>j

So, the answer is 15