(1 pt) An elementary school is offering 3 language classes: one in Spanish, one

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 100 students in the school. There are 41 in the Spanish class, 29 in the French class, and 26 in the German class. There are 13 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? It two students are chosen randomly, what is the probability that neither of them is taking a language class?

Explanation / Answer

total number =100

here let A is people taking spanish ; N french and C german class

from above:

1)number who are taking exactly 2 class

hence probability =20/100 =0.2

2)

number taking at least one class:

number not taking any class

hence probability that neither is taking a language class =(28/100)*(27/99) =0.0764

N(T)= 100 N(A)= 41 N(B)= 29 N(C)= 26 N(AnB)= 13 N(BnC)= 8 N(AnC)= 5

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