CA Foundation · Quantitative Aptitude · Probability
Two fair dice are thrown. What is the probability that the product of the two numbers shown is a perfect square?
Listing pairs whose product is a perfect square gives (1,1), (1,4), (4,1), (2,2), (3,3), (4,4), (5,5) and (6,6), which is 8 outcomes out of 36, so the probability is 8/36 = 2/9.
- A1/4
- B7/36Correct
- C1/6
- D8/36
Explanation
Products that are perfect squares: (1,1)=1, (1,4),(4,1)=4, (2,2)=4, (3,3)=9, (4,4)=16, (5,5)=25, (6,6)=36, (2,8) not possible. Count: (1,1),(1,4),(4,1),(2,2),(3,3),(4,4),(5,5),(6,6) = 8 outcomes. So probability is 8/36. Option 7/36 misses one of these outcomes.
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