Question

Two dice are thrown simultaneously. What is the probability of obtaining a multiple of $2$ on one of the them and a multiple of $3$ on the other

• A. $\frac{5}{36}$
• B. $\frac{11}{36}$
• C. $\frac{1}{6}$
• D. $\frac{1}{3}$

Answer 1

The correct option is B

$\frac{11}{36}$

Explanation for the correct option:

If two dice are rolled, total number of sample space $=6^2=36$

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

Favorable outcomes $=\left\{(2,3)(2,6)(4,3)(4,6)(6,3)(6,6)(3,2)(3,4)(3,6)(6,2)(6,4)\right\}=11$

Hence, the required probability $=\frac{11}{36}$

Hence, the correct option is option (B).