From a survey of 100 college students, a marketing research company found that 70 students owned iPhones, 35 owned cars, and 25 owned both cars and iPhones. (a) How many students owned either a car or an iPhone (but not both)? b) How many students do not own either a car or an iPhone?
Here are all the possibilties, with numbers of each:
Cars and iPhones: 25
iPhones only: 45
Cars only: 10
neither: 100 - 45 -25 -10 = 20
a) 55 (one of either but not both)
b) 20
To solve this problem, we can use the principle of inclusion-exclusion.
(a) To find the number of students who own either a car or an iPhone (but not both), we need to subtract the number of students who own both from the total number of students who own either a car or an iPhone.
Number of students who own either a car or an iPhone = Total number of students who own a car + Total number of students who own an iPhone - Number of students who own both
Total number of students who own a car = 35
Total number of students who own an iPhone = 70
Number of students who own both a car and an iPhone = 25
Number of students who own either a car or an iPhone = 35 + 70 - 25 = 80
Therefore, 80 students own either a car or an iPhone (but not both).
(b) To find the number of students who do not own either a car or an iPhone, we need to subtract the number of students who own either a car or an iPhone from the total number of students.
Number of students who do not own either a car or an iPhone = Total number of students - Number of students who own either a car or an iPhone
Total number of students = 100
Number of students who own either a car or an iPhone = 80
Number of students who do not own either a car or an iPhone = 100 - 80 = 20
Therefore, 20 students do not own either a car or an iPhone.
To solve this problem, we can use the principle of inclusion-exclusion.
Let's break down the information given in the question:
- 70 students own iPhones
- 35 students own cars
- 25 students own both cars and iPhones
(a) How many students owned either a car or an iPhone (but not both)?
To find the number of students who own either a car or an iPhone, we need to subtract the number of students who own both from the total number of students who own cars and/or iPhones.
To calculate this, we can use the formula:
Total = iPhone + Car - Both
Total = 70 + 35 - 25
Total = 80 students
So, 80 students own either a car or an iPhone (but not both).
(b) How many students do not own either a car or an iPhone?
To find the number of students who do not own either a car or an iPhone, we need to subtract the number of students who own at least one of them from the total number of students.
To calculate this, we can subtract the answer from part (a) from the total number of students, which is 100.
Number of students who do not own either a car or an iPhone = Total students - Students who own either a car or an iPhone
Number of students who do not own either a car or an iPhone = 100 - 80
Number of students who do not own either a car or an iPhone = 20 students
So, 20 students do not own either a car or an iPhone.