Chapter 13.1, Problem 27AYU

Analyzing Survey Data In a consumer survey of 500 people, 200 indicated that they would be buying a major appliance within the next month, 150 indicated that they would buy a car, and 25 said that they would purchase both a major appliance and a car. How many will purchase neither? How many will purchase only a car?

To determine

To find: How many will purchase neither? How many will purchase only a car?

Answer to Problem 27AYU

$n\left(\text{purchase neither}\right)=175$

$n\left(\text{purchase only a car}\right)=125$

Explanation of Solution

Given:

In a consumer survey of 500 people, 200 indicated that they would be buying a major appliance within the next month, 150 indicated that they would buy a car, and 25 said that they would purchase both a major appliance and a car.

Formula used:

$n\left(A\cup B\right)=n\left(A\right)+n\left(B\right)-n\left(A\cap B\right)$

Calculation:

From the given data $U=500$,

$n\left(A\right)=200$, Where $A$ defines the number of people who would be buying a major appliance.

$n\left(B\right)=150$, Where $B$ defines the number of people who would buy a car.

$n\left(A\cap B\right)=25$

$n\left(A\cup B\right)=n\left(A\right)+n\left(B\right)-n\left(A\cap B\right)$

$n\left(A\cup B\right)=200+150-25$

$n\left(A\cup B\right)=325$

Number of people who will purchase neither $=n\left(U\right)-n\left(A\cup B\right)=500-325=175$.

Number of people who will purchase only a car $=n\left(B\right)-n\left(A\cap B\right)=150-25=125$.