From the integers 1 to 16 (inclusive), a single number is selected uniformly at random. What is the probability that the chosen number is a prime?

Introduction / Context:
Prime-number selection questions are standard in basic probability. We pick one number uniformly from a finite set and ask for the probability that it satisfies a property (being prime). The solution reduces to counting favourable outcomes over total outcomes.

Given Data / Assumptions:

• Sample space: integers 1 through 16 inclusive.
• Each integer is equally likely.
• Primes are integers greater than 1 with exactly two positive divisors: 1 and itself.

Concept / Approach:
Probability = (number of favourable outcomes) / (total outcomes). We identify all primes in 1..16 and divide their count by 16.

Step-by-Step Solution:
List 1..16: 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16.Primes in this range are 2, 3, 5, 7, 11, 13 → 6 primes.Total outcomes = 16; favourable = 6 → probability = 6/16 = 3/8.

Verification / Alternative check:
Double-check the non-primes: 1 (neither prime nor composite); 4,6,8,9,10,12,14,15,16 are composite. This confirms exactly 6 primes remain.

Why Other Options Are Wrong:
1/16 assumes only one prime; 5/8 = 10/16 overcounts; 7/16 = 7 primes (incorrect, we have 6).

Common Pitfalls:
Erroneously treating 1 as prime; forgetting 9 and 15 are composite (divisible by 3).

Final Answer:
3/8