From a survey of 100 college students, a marketing research company found that 60 students owned iPods, 50 owned cars, and 20 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
Are you supposed to do these with Venn diagrams?
If so, draw two intersecting circles, name one P the other one C (for pod and car)
place 20 in the intersection of the two circles
There are supposed to be 60 in the P circle, but we already have 20 of those accounted for.
So put 40 in the P circle which does not intersect the other circle
There are supposed to be 50 in the C circle, but we have already placed 20 of those, so put 30 in the C circle not intersecting with any of the other.
number of students in the C and P circle , but not in the intersection is
40 + 30 = 70
The total I see in both circles is 40 + 20 + 30 = 90
But 100 students were surveyed, so
10 students are not in either circle, thus
10 students do not own a car or Ipod
Oh, those poor two students! Looks like they'll have to stick to walking and listening to music on their non-existent iPods. But hey, at least they won't have to worry about parking tickets or finding a charger for their device!
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) The number of students who owned either a car or an iPod (but not both) can be calculated as:
Number of students who owned either a car or an iPod = Number of students who owned a car + Number of students who owned an iPod - Number of students who owned both
Number of students who owned either a car or an iPod = 50 + 60 - 20
Number of students who owned either a car or an iPod = 90
Therefore, 90 students owned either a car or an iPod (but not both).
(b) The number of students who do not own either a car or an iPod can be calculated as:
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
Number of students who do not own either a car or an iPod = 100 - (Number of students who owned a car + Number of students who owned an iPod - Number of students who owned both)
Number of students who do not own either a car or an iPod = 100 - (50 + 60 - 20)
Number of students who do not own either a car or an iPod = 100 - 90
Number of students who do not own either a car or an iPod = 10
Therefore, 10 students do not own either a car or an iPod.
To find the number of students who owned either a car or an iPod (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 iPod.
Let's break down the information given:
Total number of students surveyed = 100
Number of students who owned iPods = 60
Number of students who owned cars = 50
Number of students who owned both cars and iPods = 20
(a) To calculate the number of students who owned either a car or an iPod (but not both), we can use the formula:
Number of students who owned either a car or an iPod (but not both) = (Number of students who owned cars) + (Number of students who owned iPods) - (Number of students who owned both cars and iPods)
Number of students who owned either a car or an iPod (but not both) = 50 + 60 - 20 = 90 - 20 = 70 students
Therefore, 70 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, we subtract the number of students who owned either a car or an iPod from the total number of students surveyed.
Number of students who do not own either a car or an iPod = Total number of students surveyed - Number of students who owned either a car or an iPod
Number of students who do not own either a car or an iPod = 100 - 70 = 30 students
Therefore, 30 students do not own either a car or an iPod.