Question

When two dice are thrown simultaneously, the probability that the sum of the two numbers that turn up is less than $11$ is:

• A. $\frac{11}{12}$
• B. $\frac{1}{12}$
• C. $\frac{2}{12}$
• D. $\frac{1}{8}$

Answer 1

Answer: (A)

$\frac{11}{12}$

Given: two dice are thrown

To find: the probability that the sum of the two numbers that turn up is less than $11$

According to the question $n\left(S\right)=6\times 6=36$

Favourable outcomes for sum less than $11$ is $\left\{\right(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(6,1),(6,2),(6,3),(6,4\left)\right\}$

$\Rightarrow n\left(E\right)=33$

Hence, the probability of getting a total less than $11$ is $\frac{n\left(E\right)}{n\left(S\right)}=\frac{33}{36}=\frac{11}{12}$