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.

Question

How many people go by neither car nor bicycle?

Answer 1

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}.