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) $\frac{5}{6}$
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