Question

Three identical dice are thrown. What is the probability of getting a total of $15$?

• A. $\frac{3}{108}$
• B. $\frac{4}{108}$
• C. $\frac{5}{108}$
• D. $\frac{6}{108}$

Answer 1

Answer: (C)

$\frac{5}{108}$

$n\left(S\right)=\mathrm{6.6.6}=216$

Event space for getting a total of 15 is

$E=\{(3,6,6),(6,3,6),(6,6,3),(6,5,4),(6,4,5),(4,5,6),(5,4,6),(5,6,4),(4,6,5),(5,5,5)\}\therefore n\left(E\right)=10$

And required probability $=\frac{10}{216}=\frac{5}{108}=\frac{10}{216}=\frac{5}{108}$