An elementary school is offering 3 language classes: one in Spanish, one in Fren

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 89 students in the school. There are 28 in the Spanish class. 29 in the French class, and 16 in the German class. There are 10 students that in both Spanish and French, 4 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 a language class?

Explanation / Answer

Total number of students= 89

No of students taking exactly 2 classes = 10+4+8-2 = 20

P(student taking exactly 2 classes) = 20/89 = 0.225

No of students taking language classes

= 28+29+16-(10+4+8-2) = 53

P(student not taking a language class) = (89-53)/89 = 0.404

So, if 2 students are taken randomly, P(both not taking language class) = 0.404x0.404 = 0.164

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