Question

A college survey was taken to determine where students study. Of 122 students surveyed, 79 studied in the cafeteria, 56 studied in the student union, 24 studied in both the student union and cafeteria. Of those interviewed how many did not study in either the cafeteria or the student union?

Answer 1

Given:

Total number of students surveyed= 122

Studied in the cafeteria = 79

Studied in the student union = 56

Studied in both the student union and cafeteria = 24

To find:

Number of student those are did not study in either the cafeteria or the student union.

Solution:

Let A be the event that student studied in the cafeteria.

B be the event that student studied in the student union.

According to the question,

$n(S)=122$, where S is sample space.

$n(A)=79$

$n(B)=56$

$n(A\cap B)=24$

Now,

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

$n(A\cup B)=79+56-24$

$n(A\cup B)=111$

So, 111 students studied in either the student union or cafeteria.

$n(A\cup B)=n(S)-n(A\cup B)$

$n((A\cup B)')=122-111$

$n((A\cup B)')=11$

Therefore, 11 students not study in either the cafeteria or the student union.