From a survey of 200 college students, a marketing research company found that 140 students owned iPhones, 75 owned cars, and 60 owned both cars and iPhones.
(a) How many students owned either a car or an iPhone (but not both)?
1 students
(b) How many students do not own either a car or an iPhone?
2 students
Number(P or C) = number(P) + number(C) - number(P and C)
= 140 + 75 - 60 = 155
number (NOT(PorC)) = 200-155 = 45
OR
Make a Venn diagram of 2 intersecting circles inside a rectangle, labeling them P and C for phone and car
place 60 inside the intersection of the two circles
There are 140 with phones, but of those 60 have already been placed, so put 80 in circle P outside the intersection part.
There are 75 with cars, but of those 60 have already been placed, so put 15 in circle C outside the intersection part.
The sum of the entries so far is 155, so 155 have either a phone or a car.
a) To get the number of either phone OR Car, but not both would be 80+15 = 95
b) the number of have neither phone nor car
= 200-155 = 45
To find the number of students who owned either a car or an iPhone (but not both), we need to subtract the number of students who owned both from the total number of students who owned either a car or an iPhone.
(a) Number of students who owned either a car or an iPhone:
Total number of students who owned a car + Total number of students who owned an iPhone - Number of students who owned both cars and iPhones
Total number of students who owned a car = 75
Total number of students who owned an iPhone = 140
Number of students who owned both cars and iPhones = 60
Number of students who owned either a car or an iPhone = 75 + 140 - 60 = 155
Therefore, 155 students owned 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 subtract the number of students who own either a car or an iPhone from the total number of students.
Total number of students = 200
Number of students who owned either a car or an iPhone = 155
Number of students who do not own either a car or an iPhone = Total number of students - Number of students who owned either a car or an iPhone
Number of students who do not own either a car or an iPhone = 200 - 155 = 45
Therefore, 45 students do not own either a car or an iPhone.