Question

If two dice are rolled find the probability that numbers coming up on both the dice will be multiples of $3$

• A. $\frac{1}{9}$
• B. $\frac{1}{18}$
• C. $\frac{1}{36}$
• D. $\frac{1}{12}$

Answer 1

The correct option is A $\frac{1}{9}$

When two dice are rolled, total number of outcomes $=6\times 6=36$
Out of these outcomes, both numbers being multiples of $3$ are $(3,3),(3,6),(6,3),(6,6)$ which are $4$ in all.
Now, probability that numbers coming up on both the dice will be multiples of $3$

$=\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}=\frac{4}{36}=\frac{1}{9}$