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 the square of a prime number p, since the divisors are 1, p, and p². Students must identify all primes whose squares lie in [100, 999], then divide by the total count of 3-digit numbers (900).
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