Question

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

Answer 1

Each die has numbers: 1, 2, 3, 4, 5, 6. 

Since two dice are rolled, the total number of outcomes is:

6 × 6 = 36

A perfect square number is a number that can be expressed as the square of an integer. The possible perfect square numbers (within the product range of two dice) are: 

1, 4, 9, 16, 25, 36

Now, we find all pairs (x, y) where x × y results in one of these perfect squares:

Product	Possible Dice Pairs (x, y)
1	(1, 1)
4	(1, 4), (2, 2), (4, 1)
9	(1, 9) (not possible), (3, 3)
16	(4, 4)
25	(5, 5)
36	(6, 6)

Thus, the favourable outcomes are: 

(1, 1), (1, 4), (2, 2), (4, 1), (3, 3), (4, 4), (5, 5), (6, 6)

Total favourable outcomes = 8

`P = ("Favorable Outcomes")/("Total Outcomes") = 8/36 = 2/9`