A survey of 1200 people in a certain city indicates that 830 own microwave​ ovens, 720 own DVD​ players, and 570 own microwave ovens and DVD players.

Question

A survey of 1200 people in a certain city indicates that 830 own microwave​ ovens, 720 own DVD​ players, and 570 own microwave ovens and DVD players.

​(A) How many people in the survey own either a microwave oven or a DVD​ player?

​(B) How many own neither a microwave oven nor a DVD​ player?

​(C) How many own a microwave oven and do not own a DVD​ player?

Answer 1

n = 1200 people surveyed

x₁ = 830 own microwave ovens

x₂ = 720 own DVD players

x₃ = 570 own microwave ovens and DVD players

(A) Add up the number of people who own just microwave ovens and just DVD players: 830 + 720 = 1550

Then subtract that by 570 to get the following: 1550 - 570 = 980

980 people own either a microwave oven or a DVD player.

(B) Subtract the total number of people surveyed by the number of people who own one of the items:

1200 - 980 = 220

220 people own neither a microwave oven nor a DVD player.

(C) Subtract the number of people who own a microwave oven by the number of people who own either one: 980 - 570 = 410

410 people own a microwave oven and not own a DVD player.