Question

Three dice are rolled. The probability that the same number will appear on each of them is

• A. $\frac{1}{36}$
• B. $\frac{1}{12}$
• C. $\frac{2}{49}$
• D. None

Answer 1

The correct option is A $\frac{1}{36}$

Solution:- (A) $\frac{1}{36}$

Let $A$ be the event that the same no. will appear on each of the dice.

Three dice can fall in $216$ ways.

Thus, $n\left(S\right)=216$

If the same number appears on each of them then the possible number of ways is $6$.

Thus $n\left(A\right)=6$

$\therefore P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}=\frac{6}{216}=\frac{1}{36}$

Hence the probability that the same number will appear on each of them is $\frac{1}{36}$.