In a school of 120 students, 68 chose A, 57 chose B, and 31 chose both. What percentage chose at least one of A or B?
Answer and explanation
Correct answer: 78.33%
Students choosing at least one option are counted by the union formula: n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Thus the number is 68 + 57 − 31 = 94. The required percentage is (94 ÷ 120) × 100 = 78.333..., which rounds to 78.33%. The subtraction prevents students who chose both options from being counted twice. Therefore option A is correct.
Frequently asked questions
What is the correct answer to this question?
78.33%
Why is this the correct answer?
Students choosing at least one option are counted by the union formula: n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Thus the number is 68 + 57 − 31 = 94. The required percentage is (94 ÷ 120) × 100 = 78.333..., which rounds to 78.33%. The subtraction prevents students who chose both options from being counted twice. Therefore option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
