Answer to Question #251535 in Statistics and Probability for Kikay

Question

A survey on subjects being taken by 250 college students in La Union revealed the following information: (Subject-number of students taking the subject) Mathematics - 145; Filipino - 90; English - 88; Math and Filipino - 25; Filipino and English - 38; Math and English - 59; Math, Filipino and English - 15. How many did not take any of the three subjects?

Answer 1

$$N(U)=250, N(M)=145, N(F)=90, N(E)=88,$$

$$N(M\cap F)=25, N(M\cap E)=59, N(F\cap E)=38,$$

$$N(M\cap F\cap E)=15$$

$$N(M\cup F\cup E)=N(M)+N(F)+N(E)$$

$$-N(M\cap F)-N(M\cap E)-N(F\cap E)$$

$$+N(M\cap F\cap E)=145+90+88$$

$$-25-59-38+15=216$$

$$N(\overline{M\cup F\cup E})=N(U)-N(M\cup F\cup E)$$

$$=250-216=34$$

34 students did not take any of the three subjects.