Question

if two fair dice are thrown simultaneously. then what is the probability that sum of the numbers appearing on the top faces of the dice is less than 4?

Answer 1

The total number of possible outcomes when 2 dies are rolled is 6^2=36
Of these the sum is less than 4 is 1+1 1+2 2+1 so the probability of getting sum less than 4 is 3/36=1/12

Answer 2

$\bold{\frac{1}{12}}$ is the probability that the sum of the number appearing on the top faces of the dice is less than 4.

Given:

Two dice are rolled together

To find:  

The probability that sum of the numbers appearing on the top faces of the dice is less than 4

Solution:

Two dice are rolled together

Hence the sample space, $n(S) = 6 \times 6 = 36$

Let A be the probability that sum of the numbers appearing on the top faces of the dice is less than 4, hence

$A = [(1,1) , (1,2) , (2,1)}$

$n(A) = 3$

P(A) =$\frac{ (n(A))}{(n(S))}$ = $\frac{3}{36}$ = $\frac{1}{12}$

The probability that sum of the numbers appearing on the top faces of the dice is less than 4 is $\bold{\frac{1}{12}}$