Question

Two dice are rolled simultaneously. The probability of getting a multiple of $2$ on one dice and a multiple of $3$ on the other is:

• A. $\frac{15}{36}$
• B. $\frac{25}{52}$
• C. $\frac{11}{36}$
• D. $\frac{5}{6}$

Answer 1

The correct option is C

$\frac{11}{36}$

Explanation for the correct option:

Finding the required probability:

On rolling a die, the possible no. of outcomes is $6$. So, rolling two dice, the possible no. of outcomes will be $6\times 6$.

Let $S$ be the set of all possible outcomes.

$\Rightarrow n\left(S\right)=6\times 6=36$

Let $A$ be the event of getting a multiple of $2$ on one die and a multiple of $3$ on the other.

$$\begin{gathered} \Rightarrow A=\left\{\left(2,3\right),\left(2,6\right),\left(4,3\right),\left(4,6\right),\left(6,3\right),\left(3,2\right),\left(3,4\right),\left(3,6\right),\left(6,2\right),\left(6,4\right),\left(6,6\right)\right\} \\ \Rightarrow n\left(A\right)=11 \end{gathered}$$

Therefore, the required probability $P\left(A\right)$ will be $\frac{n\left(A\right)}{n\left(S\right)}=\frac{11}{36}$.

Hence, the correct answer is option C.