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

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Solution

On throwing 2 dice the total number of outcomes is 36.
Out of these 36 outcomes we need to find the probability of getting the product of two numbers on the dices is a perfect square
Such outcomes are as shown:
(1, 1), (1, 4), (2, 2), (3, 3), (4, 1), (4, 4), (5, 5), (6, 6)
Number of favorable outcomes = 8
Probability of getting the numbers whose product is a perfect square on the dice = 8 / 36
= 2 / 9

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[CBSE 2014]

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