Chapter 13.1, Problem 28AYU

Analyzing Survey Data In a student survey, 200 indicated that they would attend Summer Session I, and 150 indicated Summer Session II. If 75 students plan to attend both summer sessions, and 275 indicated that they would attend neither session, how many students participated in the survey?

To determine

To find: How many students participated in the survey?

Answer to Problem 28AYU

550 students participated in the survey.

Explanation of Solution

Given:

In a student survey, 200 indicated that they would attend Summer Session I, and 150 indicated Summer Session II. If 75 students plan to attend both summer sessions, and 275 indicated that they would attend neither session.

Formula used:

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

$n(\cup )=n\left(A\cup B\right)+n\left(\overline{A\cup B}\right)$

Calculation:

From the given data,

$n\left(A\right)=200$, Where $A$ defines the number of people who would attend Summer Session I.

$n\left(B\right)=150$, Where $B$ defines the number of people who would attend Summer Session II.

$n\left(A\cap B\right)=75$

$n\left(\overline{A\cup B}\right)=275$

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

$n\left(A\cup B\right)=200+150-75$

$n\left(A\cup B\right)=275$

$n(\cup )=n\left(A\cup B\right)+n\left(\overline{A\cup B}\right)$

$n(\cup )=275+275=550$

550 students participated in the survey.