When an unbiased six-faced die is tossed, what is the probability that the outcome is a composite number?

Introduction / Context:The sample space for a single fair die roll is {1,2,3,4,5,6}. We classify which outcomes are composite and compute the probability accordingly.

Given Data / Assumptions:

• Composite numbers have more than two positive divisors.
• 1 is neither prime nor composite.

Concept / Approach:Identify composite outcomes, count them, and divide by 6.

Step-by-Step Solution:Outcomes: 1,2,3,4,5,6.Composite among these: 4 (2*2) and 6 (2*3).Count = 2; probability = 2/6 = 1/3.

Verification / Alternative check:Prime outcomes: 2,3,5 (3 outcomes). 3 primes + 2 composites + 1 neither = 6 total.

Why Other Options Are Wrong:1/2 would require 3 composites; 1/4 would require only 1 composite; 1 is impossible for a proper subset event.

Common Pitfalls:Including 1 as composite or missing that 4 and 6 are the only composites on a standard die.

Final Answer:1/3