From cards numbered 1 to 17, one card is drawn at random. What is the probability that the number is divisible by 3 or by 7?

Introduction / Context:We apply inclusion–exclusion for divisibility conditions over a finite range. Count multiples of 3, multiples of 7, then subtract overlaps (if any).

Given Data / Assumptions:

• Numbers 1,2,…,17 (uniformly likely).
• Event: divisible by 3 or by 7.

Concept / Approach:Count: ⌊17/3⌋ = 5 (3,6,9,12,15), ⌊17/7⌋ = 2 (7,14), and overlap ⌊17/21⌋ = 0 since 21 > 17. Total favorable = 5 + 2 = 7, total outcomes 17.

Step-by-Step Solution:

Verification / Alternative check:Explicit list confirms the count: {3,6,7,9,12,14,15} has size 7.

Why Other Options Are Wrong:10/17 would require 10 favorable numbers; 2/17 or 1/7 are not supported by counts.

Common Pitfalls:Forgetting to subtract overlaps (not applicable here but critical in general) or miscounting the edge near 17.

Final Answer:7/17