In a recent survey of monetary donations made by college graduates, the following information was obtained: 91 graduates had donated to a political campaign, 76 had donated to assist medical research, 131 had donated to help preserve the environment, 27 had donated to all three, 24 had donated to none of the three, 32 had donated to a political campaign and to medical research, 48 had donated to medical research and to preserve the environment, and 56 had donated to a political campaign and to p

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Question:


In a recent survey of monetary donations made by college graduates, the following information was obtained: 91 graduates had donated to a political campaign, 76 had donated to assist medical research, 131 had donated to help preserve the environment, 27 had donated to all three, 24 had donated to none of the three, 32 had donated to a political campaign and to medical research, 48 had donated to medical research and to preserve the environment, and 56 had donated to a political campaign and to preserve the environment. (Round your answers to one decimal place.)
(a) What percent of the college graduates donated to none of the three listed causes?
(b) What percent of the college graduates donated to exactly one of the three listed causes?

Answers

Answer: a) 11.26% and b) 50.23%Step-by-step explanation:Number of graduates donated to a political campaign n(A) = 91Number of graduates donated to assist medical research n(B) = 76Number of graduated to help preserve the environment n(C) = 131Number of graduated donated to all n(A∩B∩C) = 27Number of graduates donated to none = 24Number of graduated donated to political campaign and to medical research n(A∩B) = 32Number of graduates donated to medical research and to preserve the environment n(B∩C) = 48Number of graduates  donated to a political campaign and to preserve the environment n(C∩A) = 56Now, n(U)=n(A)+n(B)+n(C)-n(A∩B)-n(B∩C) -n(C∩A)+n(A∩B∩C)+n(none)[tex]n(U)=91+76+131-32-48-56+27+24=213[/tex]So, What percent of the college graduates donated to none of the three listed causes?Percentage would be [tex]\dfrac{24}{213}\times 100\\\\=11.26\%[/tex](b) What percent of the college graduates donated to exactly one of the three listed causes?Exactly one = 91+76+131-2(32-56-48)+3(27)=107Percentage would be [tex]\dfrac{107}{213}\times 100\\\\=50.23\%[/tex]Hence, a) 11.26% and b) 50.23%

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