The probability that a randomly chosen 3 digit number has exactly 3 factors :
Step-by-Step Solution
Key Concept: A number has exactly 3 factors if and only if it is of the form p² where p is prime (factors: 1, p, p²). Students must identify all 3-digit perfect squares of primes p where 100 ≤ p² ≤ 999, which means 10 ≤ p ≤ 31, and count prime values in this range.
A number has exactly 3 factors if and only if it is the square of a prime. The 3-digit squares of primes are $11^2, 13^2, 17^2, 19^2, 23^2, 29^2, 31^2$, giving 7 such numbers. The probability is $ rac{7}{900}$.
Correct Answer: 2