Question

In a single throw of two dice, what is the probability of getting a sum of $10$?

• A. $\frac{1}{12}$
• B. $\frac{1}{36}$
• C. $\frac{1}{6}$
• D. $\frac{5}{12}$

Answer 1

The correct option is A $\frac{1}{12}$

Sample ways of $2$ dice is

$(1,1);(1,2);...;(1,6)$

$(2,1);(2,2);...;(2,6)$

$(3,1);(3,2);...;(3,6)$

$(4,1);(4,2);...;(4,6)$

$(5,1);(5,2);...;(5,6)$

$(6,1);(6,2);...;(6,6)$

No of ways in which we get sum of number on $2$ dice $=10$ is

$(4,6);(5,5);(6,4)=3$ ways

$\therefore$ Probability of getting a sum of number on dices $=10$ is

$\frac{3}{36}=\frac{1}{12}$