Question

A survey of 256 USF students was taken at registration. Of those surveyed:70 students had signed up for a Math course53 students had signed up for a Language Arts course36 students had signed up for a Humanities course15 students had signed up for both a Math and Language Arts course8 students had signed up for both a Math and Humanities course5 students had signed up for both a Language Arts and Humanities course1 students had signed up for all three coursesHow many students had not signed up for any of these three courses?

Answer 1

Total number of students surveyed (μ) = 256

Number signed up for:

Math course n(M) =

Language Arts course, n(L)= 53

Humanities Course, n(H) = 36

Math and Language Arts, n(MnL) = 15

Math and Hmanities, n(MnH) = 8

Language Arts and Humanities, n(LnH) = 5

All three courses, n(MnLnH) = 1

Draw a Venn diagram for the data above:

Let the number of students that had not signed up for any of the three courses be x.

Hence,

$\begin{gathered} x=256-(48+14+34+7+1+4+24) \\ x=256-132 \\ x=124 \end{gathered}$

Therefore, the number of students that had not signed up for any of these three courses is 124