In a sports survey, 80 people like cricket, 64 like football, and 29 like both. How many like exactly one sport?
Answer and explanation
Correct answer: 86
Let C represent people who like cricket and F represent people who like football. The cricket-only group has 80 − 29 = 51 people, and the football-only group has 64 − 29 = 35 people. Exactly one sport means belonging to one set but not both, so the required total is 51 + 35 = 86. Equivalently, n(C) + n(F) − 2n(C ∩ F) = 80 + 64 − 58 = 86.
Frequently asked questions
What is the correct answer to this question?
86
Why is this the correct answer?
Let C represent people who like cricket and F represent people who like football. The cricket-only group has 80 − 29 = 51 people, and the football-only group has 64 − 29 = 35 people. Exactly one sport means belonging to one set but not both, so the required total is 51 + 35 = 86. Equivalently, n(C) + n(F) − 2n(C ∩ F) = 80 + 64 − 58 = 86.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
