If an integer is chosen uniformly from 1 to 100, what is the probability it is divisible by some perfect square greater than 1 (i.e., not squarefree)?
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Get StartedIf an integer is chosen uniformly from 1 to 100, what is the probability it is divisible by some perfect square greater than 1 (i.e., not squarefree)?
Options:
- 39/100
- 61/100
- 25/100
- 50/100
Correct answer: 39/100
Explanation: Counting squarefree numbers up to 100 via μ(k): 61 are squarefree, so 100−61 = 39 integers are divisible by a square; probability = 39/100.
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