# math

107 total foreign language students
42 take spanish
46 take french
45 take german
8 take spanish & french but not german
6 take french & german but not spanish
8 take spanish & german but not french
24 students are taking at least 2 languages

What is the probability that a student randomly selected from those taking any language does take all three languages in this semester?

What is the probability that a student randomly selected from those taking exactly one language takes French in this semester?

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1. well, 24 are taking at least two languages, if you add the above taking 2 languages, you get 8+8+6=22, which means 2 are taking three languages.

Pr(all three)=2/106

well, 42 are taking french, but of those, 6 are taking german as well, 2 are taking spanish and german, and 8 are taking spanish with french.

Pr(only French)= (42-6-2-8)/(106-24-2)

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