Question

What is the probability of getting a sum of 15, if 3 dice are thrown simultaneously?

• A. $\frac{3}{108}$
• B. $\frac{15}{216}$
• C. $\frac{5}{216}$
• D. $\frac{5}{108}$

Answer 1

The correct option is D $\frac{5}{108}$

Given three dice are thrown simultaneously.
Total number of outcomes $=6\times 6\times 6=216$

Favourable outcomes of getting a sum of 15 $=(3,6,6),(4,6,5),(5,6,4),(6,6,3),(6,3,6),(6,4,5),(6,5,4),(4,5,6),(5,5,5),(5,4,6)$

Number of favourable outcomes for getting a sum of 15 = 10

Probability of an event of getting a sum of 15 when three dice are thrown simultaneously $=\frac{10}{216}=\frac{5}{108}$