Question

The probability of the product of a perfect square when$2$dice are thrown together, is:

• A. $\frac{2}{9}$
• B. $\frac{1}{9}$
• C. $\frac{5}{18}$
• D. None of these

Answer 1

The correct option is A

$\frac{2}{9}$

Explanation for correct option

Finding the probability:

When two dice are thrown, the number of sample spaces obtained is $36$.

Favorable outcomes $=\left\{\left(1,1\right),(2,2),(4,1),(1,4),(3,3),(4,4),(5,5),(6,6)\right\}$

Therefore, the required probability is:

$$\begin{gathered} =\frac{\mathrm{Favourable}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}} \\ =\frac{8}{36} \\ =\frac{2}{9} \end{gathered}$$

Therefore, the correct answer is option (A).