math
posted by Kelly on .
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?

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)= (42628)/(106242)