Suppose that in a town , 800 people are selected by random types of sampling methods. 280 go to work by car only,220 go to work by bicycle only and 140 ) use both ways - sometimes go with a car and sometimes with a bicycle.

Question

find
How many people go to work by car only?
How many people go to work by bicycle only?
How many people go by neither car nor bicycle?
How many people use at least one of both transportation types?
How many people use only one of car or bicycle?

Answer 1

To find the numbers of people using different transportation methods, we can use the principle of inclusion-exclusion.

Let:
A = number of people who go to work by car only
B = number of people who go to work by bicycle only
C = number of people who use both ways
N = total number of people surveyed (800)

Given:
N = 800
A = 280
B = 220
C = 140

1. Number of people who go to work by car only = A = 280

2. Number of people who go to work by bicycle only = B = 220

3. Number of people who go by neither car nor bicycle can be found by:
Total number of people who use at least one of both transportation types = A + B - C
= 280 + 220 - 140
= 360
Therefore, number of people who go by neither car nor bicycle = N - (A + B - C)
= 800 - 360
= 440

4. Number of people who use at least one of both transportation types = A + B - C
= 360

5. Number of people who use only one of car or bicycle:
Number of people who use only car = A - C (people who use both ways)
= 280 - 140
= 140
Number of people who use only bicycle = B - C (people who use both ways)
= 220 - 140
= 80

Therefore, number of people who use only one of car or bicycle = 140 (only car) + 80 (only bicycle) = 220