A company that specializes in languages lists the following information concerni

Question

A company that specializes in languages lists the following information concerning its English-speaking employees: 23 employees speak German; 27 speak French; 33 speak Spanish; 43 speak Spanish or French; 34 speak French or German; 48 speak German or Spanish; 8 speak Spanish, French, and German; and 7 speak English only. (Round your answer to one decimal place.)

b. What percent of the employees speak at least one language other than English?

b. What percent of the employees speak at least two languages other than English?

Explanation / Answer

23 employees speak German; 27 speak French; 33 speak Spanish;

43 speak Spanish or French; So, 27+33-43 = 17 speak both French and Spanish

34 speak French or German; So, 27+23-34 = 16 speak both French and German

48 speak German or Spanish; So, 27+33-48 = 12 speak both Spanish and German

8 speak Spanish, French, and German; and 7 speak English only

a. P( atleast 1 language other than English) = (23+27+33)-17-16-12+8 = 46

But total is 46+only english = 46+7 = 53

So, percent of the employees speak at least one language other than English = 46/53 = 86.8%

b. P( atleast 2 languages other than English) = P( 2 , 3 languages) = 17+16+12-2*8 / 53 = 54.72%

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