Question

On rolling a pair of dice, what is the probability of getting the same number on both the dice?

• A. True
• B. False
• C. $\frac{1}{3}$
• D. $\frac{1}{2}$

Answer 1

The correct option is B

False

Given,

Sample space for rolling a pair of dice = S { (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) }

$\Rightarrow$ Total number of outcomes = 36

The required outcomes are (1,1), (2,2), (3,3), (4,4), (5,5) and (6,6).

$\Rightarrow$ Number of favourable outcomes = 6

Probability of an event, P(E) = $=\frac{\text{number of favourable outcomes}}{\text{total number of outcomes}}$

P (getting the same number on both the dice) = $\frac{6}{36}=\frac{1}{6}$

Therefore, the probability of getting the same number on both the dice is $\frac{1}{6}$ .