Question

Two dice are rolled together. Find the probability of getting such numbers on two dice whose product is a perfect square.

Answer 1

When two different dice are thrown, then total number of outcomes = 36.

Let E be the event of getting the product of numbers, as a perfect square.

These numbers are (1, 1), (1, 4), (2, 2), (3, 3), (4, 1), (4, 4), (5, 5) and (6, 6).

Number of Favourable outcomes = 8

∴ P(getting the product of numbers, as a perfect square) = $\mathrm{P}\left(\mathrm{E}\right)=\frac{\mathrm{Number}\mathrm{of}\mathrm{outcomes}\mathrm{favourable}\mathrm{to}\mathrm{E}}{\mathrm{Number}\mathrm{of}\mathrm{all}\mathrm{possible}\mathrm{outcomes}}$

= $\frac{8}{36}=\frac{2}{9}$

Thus, the probability of getting the product of numbers, as a perfect square is $\frac{2}{9}$.