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)

`=P(E)="Number of outcomes favourable to E"/"Number of all possible outcome"`

`=8/36 = 2/9` 

Thus, the probability of getting the product of numbers, as a perfect square is `2/9`.