Question

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 101 students in the school. There are 33 in the Spanish class, 33 in the French class, and 23 in the German class. There are 14 students that are in both Spanish and French, 7 are in both Spanish and German, and 8 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 two language class?

If two students are chosen randomly, what is the probability that neither of them is taking Spanish?

Answer 1

Let S denote Spanish

F denote French

G denote German

n(S)=33

n(F)=33

n(G)=23

Number of students taking excatly two language class =

  

Total number of students = 101

Probability of choosing a student taking excatly two language class = 17/101=0.168

Total number of students taking spanish = 33

Probability of choosing 2 students such that both of them is taking Spanish = 33C2/101C2 = 528/5050 = 0.1045

Therefore, Probability of choosing 2 students such that niether of them is taking Spanish = 1- 0.1045 = 0.8955