Question

The probability that the same number appears on throwing three dice simultaneously is

• A. $\frac{1}{36}$
• B. $\frac{5}{36}$
• C. $\frac{1}{6}$
• D. $\frac{4}{13}$

Answer 1

The correct option is A

$\frac{1}{36}$

The explanation for the correct option

It is given that, $3$ dice with $6$ faces are rolled.

Thus, the total number of cases, $n\left(S\right)=6^3=216$.

The cases for obtaining the same numbers can be given by, $R=\left\{\left(1,1,1\right),\left(2,2,2\right),\left(3,3,3\right),\left(4,4,4\right),\left(5,5,5\right),\left(6,6,6\right)\right\}$.

Thus, the number of cases to obtain the same numbers can be given by, $n\left(R\right)=6$.

Hence, the probability of obtaining the same numbers can be given by $P\left(R\right)=\frac{n\left(R\right)}{n\left(S\right)}=\frac{6}{216}=\frac{1}{36}$.

Therefore, the probability that the same number appears on throwing three dice simultaneously is $\frac{1}{36}$. So, the correct option is (A).