Answer
550 students participated in the survey.
Work Step by Step
There are three sets of people in this exercise:
$U$ is all of the students asked in the survey.
$A$ isthe students who would attend Summer session I.
$B$ is the students who would attend Summer session II.
$n(A)=200$
$n(B)=150$
$n(A\cap B)=75$
$n(U)-n(A\cup B)=275$
Using the Counting Formula for sets:
$n(A\cup B)=n(A)+n(B)-n(A\cap B)=200+150-75=275$
275 students would attend any of these sessions; therefore, $n(U)-275=275$ would attend neither.
From this, we can calculate the number of students taking part in the survey:
$n(U)=275+275=550$
