Single correct option
A pair of fair six-sided dice is rolled once. What is the probability that the sum of the two numbers obtained is a perfect square?
- A. 1/6
- B. 7/36
- C. 5/36
- D. 1/4
Show answer and solution
Answer: (B) 7/36
Possible perfect-square sums from 2 to 12 are 4 and 9 (1 and 16 are out of range).
Sum 4: (1,3),(2,2),(3,1) → 3 outcomes. Sum 9: (3,6),(4,5),(5,4),(6,3) → 4 outcomes. Total = 7.
Probability = 7/36.
Trap: forgetting sum 9's outcomes or missing that 1 is not achievable (minimum sum is 2) leads to the wrong count.
Sum 4: (1,3),(2,2),(3,1) → 3 outcomes. Sum 9: (3,6),(4,5),(5,4),(6,3) → 4 outcomes. Total = 7.
Probability = 7/36.
Trap: forgetting sum 9's outcomes or missing that 1 is not achievable (minimum sum is 2) leads to the wrong count.
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