Question

I now have the first answer, but don’t know how to get the second one.

(1 point) An elementary school is offering 3 language classes: one in Spanish, one in French, and one in German. These classes are open to any of the 107 students in the school. There are 36 in the Spanish class, 32 in the French class, and 26 in the German class. There are 10 students that are in both Spanish and French, 6 are in both Spanish and German, and 8 are in both French and German. In addition, there are 2 students taking all 3 classes. If one student is chosen randomly, what is the probability that he or she is not in any of these classes? If two students are chosen randomly, what is the probability that neither of them is taking Spanish? Leave your answers in fraction form. You can enter exact expressions such as 10 9/(23 22) f you want to avoid typing large numbers

Answer 1

let A.B and C are number of students in Spanish;French and German class

N(T)=	107
N(A)=	36
N(B)=	32
N(C)=	26
N(AnB)=	10
N(BnC)=	8
N(AnC)=	6
N(AUB)=	58
N(BUC)=	50
N(AUC)=	56
N(AnBnC) =	2

1)

P(she or he not in any of the classes)_ =(N(T) -N(A u B u C))/N(T) =(107-72)/107 =35/107

2) P(neither is taking Spanish)=(71*70)/(107*106) (as there are 71 students who are not taking Spanish)