Question

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

Options

• \[\frac{2}{3}\]

• \[\frac{1}{6}\]

• \[\frac{1}{3}\]

• \[\frac{5}{6}\]

Answer 1

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  `6^2=36`

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" = " Number of favourablr event"/"Total number of event"`

Hence probability of getting different faces of both dice is `30/36=5/6`