Thread: Tricky Probability question.

Hi Guys - Stuck with an excersie sheet question:

n the start of new term at a language school there are 104 students. The school offers classes in French, German and Italian. If a student has previously studied French before, then they may choose to do only French, or they may study any two of the three languages. Otherwise the student must study French and one of the other language of their choice.

If there are 38 students studying Italian and another language, 37 students studying German and another langauge, and there are 72 students studying only French, how many students are studying both German and Italian?

Can anyone shed some light? I've spent about 30 mins going around in circles!

Thanks F

Note that:

(1) Nobody studies all three languages.
(2) Students studying Italian and another language = students studying Italian
(3) Students studying German and another language = students studying German
(4) #(students studying Italian or German) + #(students studying only French) = 104.

Originally Posted by emakarov

Note that:

(1) Nobody studies all three languages.
(2) Students studying Italian and another language = students studying Italian
(3) Students studying German and another language = students studying German
(4) #(students studying Italian or German) + #(students studying only French) = 104.

I sketched this as a Venn but not sure how I can eliminate anything. I assigned letters to the intersection of Italian and French, Italian and German & French and German. But this just introduces three variables and I can't eliminate any??

Another step? Or what actual figure am I working towards and I'll see if I can work backwards.

Thanks

I get "I" union "G" to be 32 by (I union G) + F = 104. Using the standard formula for non exclusive events I can't find how to get (I intersection G) as I dont know the individual values for I or G.

OK, now it seems to me that the data is contradictory. I agree that |I ∪ G| = 104 - 72 = 32. But how can this be if there are 38 students studying Italian and another language?

Originally Posted by FelixHelix

Using the standard formula for non exclusive events I can't find how to get (I intersection G) as I dont know the individual values for I or G.

You do know the individual values for I or G because of points (2) and (3) in post #2.

im sure im wrong lol

but 104 - 72 = 32

32 students have the potential to study german and italian

if out of the 32 students 38 study italian and out of 32 students 37 study german

then logically all 32 students study german and italian