# Two dice are rolled simultaneously.

Question:

Two dice are rolled simultaneously. The probability that they show different faces is

(a) $\frac{2}{3}$

(b) $\frac{1}{6}$

(c) $\frac{1}{3}$

(d) $\frac{5}{6}$

Solution:

GIVEN: A pair of dice is thrown

TO FIND: Probability of getting different faces

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

Favorable events i.e. getting different faces of both dice are

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

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

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

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

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

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

Hence total number of favorable events i.e. getting different faces of both dice is 30

We know that PROBABILITY =

Hence probability of getting different faces of both dice is

Hence the correct option is