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: $n(U)=275+275=550$