Please help! Due half an hour exactly! 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 97 students in the school. There are 34 in the Spanish class, 37 in the French class, and 21 in the German class. There are 16 students that in both Spanish and French, 6 are in both Spanish and German, and 7 are in both French and German. In addition, there are 3 students taking all 3 classes.
(a) If one student is chosen randomly, what is the probability that he or she is not in any of these classes?

Question

Please help! Due half an hour exactly! 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 97 students in the school. There are 34 in the Spanish class, 37 in the French class, and 21 in the German class. There are 16 students that in both Spanish and French, 6 are in both Spanish and German, and 7 are in both French and German. In addition, there are 3 students taking all 3 classes. 
(a) If one student is chosen randomly, what is the probability that he or she is not in any of these classes?

anonymous · Answer

(b) If two students are chosen randomly, what is the probability that at least one of them is taking German?

anonymous · Answer

(a) If you do your Venn Diagram, you see that only 66 students are taking at least one of the classes. There are 31 students out of 97 who are not taking any of the 3 classes. Hence the answer is $$ \frac {31}{97}$$

anonymous · Answer

(b)
$$ 2\frac {21}{97 }-  \frac {21}{97 }\frac {20}{96 }=\frac{301}{776}
$$