Question

If three six faced fair dice are thrown together, then the probability that the sum of three appearing on the dice is k (9 < k < 14) is

• A. $\frac{20}{226}$
• B. $\frac{29}{216}$
• C. $\frac{24}{214}$
• D. $\frac{27}{216}$

Answer 1

The correct option is D $\frac{27}{216}$

Total cases$=6^3=216$

Let's check options for $k=10$

(A) $\frac{100-210+183}{216}-\frac{-27}{216}<0$ probability $\ge 0$

(B) Same as (A)

(C) $\frac{210-100-83}{216}=\frac{27}{216}$ can be answer.

As (C) and (D) are exactly same $\Rightarrow$Both are answers.