Question

9-1: in a survey of 400 students, 285 have a car and 320 have a bike. 63 students do not have either. create a venn diagram to represent this situation and determine the number of students in the survey who has both a car and a motorbike.

Explanation:

Step1: Find students with at least one vehicle

Total students: $400$; No vehicle: $63$
$400 - 63 = 337$

Step2: Apply inclusion-exclusion principle

Let $n(C)=285$ (car), $n(B)=320$ (bike), $n(C\cup B)=337$. Use $n(C\cap B)=n(C)+n(B)-n(C\cup B)$
$285 + 320 - 337 = 268$

Answer:

268