A number is chosen uniformly at random from the first 120 natural numbers. What is the probability that it is a multiple of 5 or 15?

Introduction / Context:We must count numbers divisible by 5 or 15 among 1..120. Since “multiple of 15” is a subset of “multiple of 5,” the union simplifies to just “multiple of 5.”

Given Data / Assumptions:

• Range: 1 to 120 inclusive.
• Multiples of 15 are included in multiples of 5.

Concept / Approach:Count multiples of 5: floor(120/5). Divide by 120 to get probability.

Step-by-Step Solution:Multiples of 5 in 1..120: 120/5 = 24 numbers.Probability = 24 / 120 = 1/5.

Verification / Alternative check:Explicit list (5,10,...,120) has 24 terms; inclusion–exclusion not needed since 15-subset is contained within 5-multiples.

Why Other Options Are Wrong:1/6 and 1/8 mismatch the correct count; “None of these” is false because 1/5 is available.

Common Pitfalls:Double counting with inclusion–exclusion when one set is wholly contained in the other.

Final Answer:1/5