Question

1. 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 104 students in the school. There are 43 in the Spanish class, 34 in the French class, and 24 in the German class. There are 17 students that in both Spanish and French, 6 are in both Spanish and German, and 9 are in both French and German. In addition, there are 4 students taking all 3 classes.
If one student is chosen randomly, what is the probability that he or she is taking exactly one language class?  
If two students are chosen randomly, what is the probability that both of them are taking French?

2. A company conducted a survey of 400 of its employees. Of those surveyed, it was discovered that 133 like baseball, 49 like hockey, and 18 like both baseball and hockey. Let B denote the set of employees which like baseball and H the set of employees which like hockey.

How many employees are there in the set B∪H^c?

How many employees are in the set (B∩H)^c?

Answer 1

1)let A,B and C are students taking Spanish; French and German class,

from above:

N(T)=	104
N(A)=	43
N(B)=	34
N(C)=	24
N(AnB)=	17
N(BnC)=	9
N(AnC)=	6
N(AnBnC) =	3

exactly one class =

N(A)+N(B)+N(C )-2(N(AnB)+N(BnC)+N(AnC))+3*N(AnBnC)

=

46

therefore probability that he or she is taking exactly one language class =46/104 =23/52=0.4423

b)

probability that both of them are taking French =(34/104)*(33/103)=0.1047

2)

employees are there in the set B∪H^c =N(T)-N(H)+N(H n B)=400-49+18=369

mployees are in the set (B∩H)^c =N(T)-N( B n H) =400-18=382