Homework Help: math

Posted by Christy on Wednesday, December 15, 2010 at 1:04am.

There are a total of 107 foreign language students in a high school where they offer only Spanish, French, and German. 42 take Spanish.
46 take French.
45 take German.
8 take Spanish and French but not German.
8 take Spanish and German but no French.
6 take French and German but not Spanish.
24 students are taking at least two languages.

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

math - Reiny, Wednesday, December 15, 2010 at 8:39am
Best done with a Venn diagram.
overlap three circles called S F and G
place x in the middle for S F and G
fill in the rest of the entries
e.g. the number taking only Spanish = 42 - 8 - 8 - x
= 26-x

similarly:
only German = 45 - 8 - 6 - x = 31 - x
only French = 46 - 8 - 6 - x = 32 - x

we can find x ....
26-x +8+8+6+x+32-x+31-x = 107
-2x = -4
x = 2

so those taking only French = 32-2= 30

prob of stated event = 30/107

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