Single correct option
Two fair six-sided dice are thrown. What is the probability that the product of the two numbers is a perfect square?
- A. 1/6
- B. 7/36
- C. 2/9
- D. 1/4
Show answer and solution
Answer: (C) 2/9
Favourable outcomes:
- Equal numbers (1,1), (2,2), …, (6,6): product is a square — 6 outcomes.
- Unequal pairs with square product: only (1,4) and (4,1), since 1 × 4 = 4. (Check others: 2×8, 3×12 are impossible on a die.)
Total favourable = 8 out of 36 ⇒ probability = 2/9.
1/6 counts only the doubles; 7/36 counts (1,4) but forgets (4,1).
- Equal numbers (1,1), (2,2), …, (6,6): product is a square — 6 outcomes.
- Unequal pairs with square product: only (1,4) and (4,1), since 1 × 4 = 4. (Check others: 2×8, 3×12 are impossible on a die.)
Total favourable = 8 out of 36 ⇒ probability = 2/9.
1/6 counts only the doubles; 7/36 counts (1,4) but forgets (4,1).
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