Question:
The number is selected randomly from the integers \(1\) to \(100\). The probability that the number selected has exactly three factors is ...
The number is selected randomly from the integers \(1\) to \(100\). The probability that the number selected has exactly three factors is ...
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Only squares of primes have exactly three factors; list those up to 100.
Updated On: Nov 12, 2026
- \(\frac{1}{25}\)
- \(\frac{1}{20}\)
- \(\frac{9}{100}\)
- \(\frac{1}{10}\)
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept
A number has exactly three factors only if it is the square of a prime, since \(p^{2}\) has factors \(1,p,p^{2}\).
Step 2: List
Primes with \(p^{2}\leq 100\) are \(2,3,5,7\). So the numbers are \(4,9,25,49\), which is 4 numbers.
Step 3: Probability
\(P=\dfrac{4}{100}=\dfrac{1}{25}\).
Final Answer:
The probability is \(\dfrac{1}{25}\). \[ \boxed{\text{(A) }\dfrac{1}{25}} \]
A number has exactly three factors only if it is the square of a prime, since \(p^{2}\) has factors \(1,p,p^{2}\).
Step 2: List
Primes with \(p^{2}\leq 100\) are \(2,3,5,7\). So the numbers are \(4,9,25,49\), which is 4 numbers.
Step 3: Probability
\(P=\dfrac{4}{100}=\dfrac{1}{25}\).
Final Answer:
The probability is \(\dfrac{1}{25}\). \[ \boxed{\text{(A) }\dfrac{1}{25}} \]
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