A black die and a white die are thrown at the same time. Write all the possible outcomes. What is the probability?

that the difference of the numbers appearing on the top of two dice is 2.

#### Solution

A pair of dice is thrown

TO FIND: Probability of the following:

Let us first write the all possible events that can occur

(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),

Hence total number of events is `6^2=36`

Favourable outcomes for getting the difference of the numbers as 2 are

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

Thus, the number of favourable outcomes are 8.

∴ P(getting the difference of the numbers as 2) =\[\frac{\text{ Favourable number of outcomes }}{\text{ Total number of outcomes }} = \frac{8}{36} = \frac{2}{9}\]