Multiple choice

Probability of product of a perfect square when $2$ dice are thrown together, is

  1. $\dfrac{2}{9}$
  2. $\dfrac{1}{9}$
  3. $\dfrac{5}{18}$
  4. $None\ of\ these$
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A Correct answer
Explanation

Total outcomes = 36. Perfect squares possible from product of two dice (1-6): 1 (1x1), 4 (1x4, 4x1, 2x2), 9 (3x3), 16 (4x4), 25 (5x5), 36 (6x6). Total favorable outcomes: (1,1), (1,4), (4,1), (2,2), (3,3), (4,4), (5,5), (6,6). That is 8 outcomes. 8/36 = 2/9.

AI explanation

The total number of possible outcomes when rolling two dice is 36. The product of the two numbers is a perfect square for the outcomes (1,1), (1,4), (4,1), (2,2), (3,3), (4,4), (4,9), (5,5) and (6,6), totaling 8 favorable combinations. Therefore, the actual probability of rolling a perfect square product is 8/36, which simplifies to 2/9.

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