Each of the 20 students learns exactly two out of three languages: English, French, and German. 80% learn English and 50% French. What percentage learns German?

A- student speaks English P(A)=0.8, P(A')=0.2 F- student speaks French P(F)=0.5, P(F')=0.5

I do not know how to deal with this. I would be grateful for any hints.


1 Answer 1


Since each student learns $2$ languages, the percentage of German, French, and English learned should total $200\%$ together.

Therefore, $70\%$ learn German.

  • $\begingroup$ Thank you. Could you please explain why total is 200%? $\endgroup$
    – Uhans
    Dec 2, 2019 at 8:49
  • $\begingroup$ think about it like this; if each student learned 1 language, then it would be 20 "languages" learned by 20 students for a total of 100%, but now it's 40 "languages" learned by 20 students for a total of 200% $\endgroup$ Dec 2, 2019 at 8:51
  • $\begingroup$ Now I understand. Thanks again. $\endgroup$
    – Uhans
    Dec 2, 2019 at 8:55

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