Question

Three identical dice are thrown. What is the probability that an odd number is obtained on each die given that the sum obtained is $15$.

• A. $\frac{3}{4}$
• B. $\frac{1}{4}$
• C. $\frac{9}{10}$
• D. $\frac{1}{10}$

Answer 1

Answer: (D)

$\frac{1}{10}$

Sample space is

$S=\{(3,6,6),(6,3,6),(6,6,3),(6,5,4),(6,4,5),(4,5,6),(5,4,6),(5,6,4),(4,6,5),(5,5,5)\}$

$\therefore n\left(S\right)=10$

$E=\left[(5,5,5)\right]$

$\therefore n\left(E\right)=1$

Hence required probability $=\frac{1}{10}$