SOLUTION: 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 104 students in the school. There are 42

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Question 1175374: 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 104 students in the school. There are 42 in the Spanish class, 31 in the French class, and 16 in the German class. There are 15 students that in both Spanish and French, 4 are in both Spanish and German, and 6 are in both French and German. In addition, there are 2 students taking all 3 classes. If two students are chosen randomly, what is the probability that at least one of them is taking German?
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
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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 104 students in the school.
There are 42 in the Spanish class, 31 in the French class, and 16 in the German class.
There are 15 students that in both Spanish and French, 4 are in both Spanish and German, and 6 are in both French and German.
In addition, there are 2 students taking all 3 classes.
If two students are chosen randomly, what is the probability that at least one of them is taking German?
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This probability is the COMPLEMENT to the probability that NO ONE of the two random students is taking German.


This probability P(no one is taking German)  is  C%5B104-16%5D%5E2%2FC%5B104%5D%5E2 = C%5B88%5D%5E2%2FC%5B104%5D%5E2 = %28%28%2888%2A87%29%2F2%29%29%2F%28%28%28104%2A103%29%2F2%29%29 = 0.7147,


so the probability under the problem's question is  1 - 0.7147 = 0.2853.     ANSWER

Solved.

Notice that only the numbers 104 (all students in the class) and 16 (those taking German) is used in my solution.

The rest of data is irrelevant and is excessive and unnecessary.