From a survey of 100 college students, a marketing research company found that 65 students owned ipods, 45 owned cars, and 15 owned both cars and Ipods.
(a) How many students owned either a car or an ipod (but not both)?
(b)How many students do not own either a car or an ipod?
Number(Ipad or Car)
= number(Ipad) + number(carss) - number(Ipads and cars)
= 65 + 45 - 15 = 95
which leaves 5 unaccounted for from the 100
so ....
a) 95 owned either Ipad or car
b) 5 owned neither
or
you could get the same result by constructing a Venn diagram
To find the number of students who owned either a car or an iPod (but not both), we can subtract the number of students who owned both from the total number of students who owned either a car or an iPod.
(a) Number of students who owned either a car or an iPod (but not both) = (Total number of students who owned a car) + (Total number of students who owned an iPod) - (Number of students who owned both a car and an iPod)
Total number of students who owned a car = 45
Total number of students who owned an iPod = 65
Number of students who owned both a car and an iPod = 15
Number of students who owned either a car or an iPod (but not both) = 45 + 65 - 15 = 95
Therefore, 95 students owned either a car or an iPod (but not both).
To find the number of students who do not own either a car or an iPod, we subtract the number of students who owned either a car or an iPod (from part a) from the total number of students.
(b) Number of students who do not own either a car or an iPod = Total number of students - Number of students who owned either a car or an iPod
Total number of students = 100
Number of students who owned either a car or an iPod (from part a) = 95
Number of students who do not own either a car or an iPod = 100 - 95 = 5
Therefore, 5 students do not own either a car or an iPod.