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October 25, 2014

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

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 8:39amBest 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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