Question

When three dice are thrown the probability of getting $4$ or $5$ on each of the dice simultaneously is

• A. $\frac{1}{72}$
• B. $\frac{1}{108}$
• C. $\frac{1}{24}$
• D. None of these

Answer 1

The correct option is D

None of these

Finding the probability of getting $4$ or $5$ on each of the dice simultaneously

The total number of outcomes when $n$ number of dice are rolled is $6^n$.

If three dice are rolled, then the total number of sample space is,

$6^3=216$

The possible ways of getting $4$ or $5$ on each of the dice simultaneously are:

$445,454,455,444,544,545,554,555$

The number of favorable outcomes $=8$

So, the probability of getting $4$ or $5$ on each of the dice simultaneously is,

$P=\frac{8}{216}$

$\Rightarrow$ $P=\frac{1}{27}$

Hence, the correct option is $D)$ None of these.