From a survey of 100 college students, a marketing research company found that 85 students owned iPods, 45 owned cars, and 35 owned both cars and iPods.
(a) How many students owned either a car or an iPod (but not both)?
1 students
(b) How many students do not own either a car or an iPod?
2 students Viewing Saved Work Revert to Last Response
To find the number of students who owned either a car or an iPod (but not both), you need to subtract the number of students who owned both from the total number of students who owned either a car or an iPod.
(a) To solve this, you can use the principle of inclusion-exclusion. In this case, you know that there are 85 students who own iPods, 45 students who own cars, and 35 students who own both cars and iPods.
So, the number of students who own either a car or an iPod (but not both) can be calculated as follows:
Total number of students who own either a car or an iPod = Total number of students who own cars + Total number of students who own iPods - Total number of students who own both cars and iPods
Total number of students who own either a car or an iPod = 85 + 45 - 35
Total number of students who own either a car or an iPod = 95 students
Therefore, 95 students owned either a car or an iPod (but not both).
(b) To find the number of students who do not own either a car or an iPod, you subtract the number of students who own either a car or an iPod from the total number of students.
Total number of students who do not own either a car or an iPod = Total number of students - Total number of students who own either a car or an iPod
Total number of students who do not own either a car or an iPod = 100 - 95
Total number of students who do not own either a car or an iPod = 5 students
Therefore, 5 students do not own either a car or an iPod.