Neither-of-two percentage from two activities with overlap: In a town, 65% watch TV news, 40% read a newspaper, and 25% do both. What percentage do neither?

Introduction / Context:For two activities A and B, the union percentage is p(A) + p(B) − p(A ∩ B). The “neither” percentage is the complement of the union within 100%. This is a direct inclusion–exclusion application.

Given Data / Assumptions:

• p(TV) = 65%
• p(Newspaper) = 40%
• p(Both) = 25%

Concept / Approach:Compute union first, then subtract from 100% to get neither.

Step-by-Step Solution:Union = 65% + 40% − 25% = 80%Neither = 100% − 80% = 20%

Verification / Alternative check:Venn diagram logic: the four partitions sum to 100%; “neither” is whatever remains after accounting for the union.

Why Other Options Are Wrong:5%, 10%, 15% do not match the computed complement given the fixed union of 80%.

Common Pitfalls:Adding the given percentages without subtracting the overlap double-counts the intersection and yields 105% instead of 80%.

Final Answer:20%