Two different dice are rolled together once. Find the probability of numbers coming on the tops whose product is a perfect square.

Two dice can be thrown in 6 × 6 = 36 ways.

We have to calculate the probability of numbers coming on the tops whose product is a perfect square.

A perfect square on the dice can be obtained as

{(1, 1), (1, 4), (2, 2), (3, 3), (4,1), (4, 4), (5, 5), (6, 6)} = 8 ways.

We know that the theoretical (classical) probability of an event E, written as P (E), is defined as P (E) = Number of outcomes favorable to E / Number of all possible outcomes of the experiment

P (perfect square) = 8/36 = 2/9

Answer: The probability of numbers coming on the tops whose product is a perfect square is 2/9.