From a survey of 100 college students, a marketing research company found that 55 students owned iPods, 25 owned cars, and 15 owned both cars and iPods.
(a) How many students owned either a car or an iPod (but not both)?
55+25-15 = ?
To find out how many students owned either a car or an iPod (but not both), we need to calculate the total number of students owning either a car or an iPod and then subtract the number of students owning both.
Let's use set notation to represent the numbers:
Let A = number of students owning iPods
Let B = number of students owning cars
From the information given:
A = 55 (students owning iPods)
B = 25 (students owning cars)
Now, we know that 15 students own both cars and iPods.
To find the number of students owning either a car or an iPod (but not both), we can use the principle of inclusion-exclusion:
Total number of students owning either a car or an iPod = Number of students owning iPods + Number of students owning cars - Number of students owning both
Total number of students owning either a car or an iPod = A + B - 15
Therefore, the total number of students owning either a car or an iPod (but not both) is equal to 55 + 25 - 15 = 65.
To find the number of college 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 college students surveyed = 100
Number of students who owned iPods = 55
Number of students who owned cars = 25
Number of students who owned both cars and iPods = 15
To find the number of students who owned either a car or an iPod (but not both), we can use the principle of inclusion-exclusion.
Step 1: Find the number of students who owned either a car or an iPod:
Number of students who owned either a car or an iPod = Number of students who owned cars + Number of students who owned iPods
= 25 + 55
= 80
Step 2: Subtract the number of students who owned both cars and iPods:
Number of students who owned either a car or an iPod (but not both) = Number of students who owned either a car or an iPod - Number of students who owned both cars and iPods
= 80 - 15
= 65
Therefore, 65 college students owned either a car or an iPod (but not both).