(1 pt) 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 86 students in the school. There are 32 in the Spanish class, 31 in the French class, and 18 in the German class. There are 14 students that in both Spanish and French, 5 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 taking exactly two language classes?
If two students are chosen randomly, what is the probability that neither of them is taking Spanish?

Question

(1 pt) 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 86 students in the school. There are 32 in the Spanish class, 31 in the French class, and 18 in the German class. There are 14 students that in both Spanish and French, 5 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 taking exactly two language classes?  
If two students are chosen randomly, what is the probability that neither of them is taking Spanish?

callisto · Answer

No. of students taking Spanish +French = 14 -2 =12
No. of students taking Spanish +German = 5-2 = 3
No. of students taking German +French = 8-2 = 6

Therefore
P(taking exactly 2 language classes)  = (12+3+6) / 86
P(neither of them is taking spanish) = [(86 - 32)/ 86 ] x [(85 - 32)/85]

I'm not sure!