Suppose that in a town, 800 people are selected by random types of sampling methods. 420 go to work by car, 360 go to work by bicycle and 140 use both ways - sometimes go with a car and sometimes with a bicycle.
How many people go by neither car nor bicycle?
We can solve this problem using the principle of inclusion-exclusion.
Let A be the set of people who go to work by car, B be the set of people who go to work by bicycle, and C be the set of people who use both ways. Then, the number of people who go to work by either car or bicycle (or both) is given by:
|A ∪ B| = |A| + |B| - |A ∩ B|
where |A| denotes the cardinality (number of elements) of set A. We are given that:
|A| = 420
|B| = 360
|A ∩ B| = 140
Substituting these values, we get:
|A ∪ B| = 420 + 360 - 140 = 640
Therefore, the number of people who go to work by neither car nor bicycle is:
800 - |A ∪ B| = 800 - 640 = 160
Answer: \boxed{160}.
To find the number of people who go by neither car nor bicycle, we need to subtract the number of people who go by car, bicycle, and both ways from the total number of people.
Total number of people = 800
Number of people who go by car = 420
Number of people who go by bicycle = 360
Number of people who go by both car and bicycle = 140
To find the number of people who go by neither car nor bicycle, we can use the principle of inclusion-exclusion:
Number of people who go by neither car nor bicycle = Total number of people - (Number of people who go by car + Number of people who go by bicycle - Number of people who go by both car and bicycle)
Number of people who go by neither car nor bicycle = 800 - (420 + 360 - 140)
= 800 - (780 - 140)
= 800 - 640
= 160
Therefore, 160 people go by neither car nor bicycle.