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?

Answer 1

Answer: a) 11.26% and b) 50.23%

Step-by-step explanation:

Number of graduates donated to a political campaign n(A) = 91

Number of graduates donated to assist medical research n(B) = 76

Number of graduated to help preserve the environment n(C) = 131

Number of graduated donated to all n(A∩B∩C) = 27

Number of graduates donated to none = 24

Number of graduated donated to political campaign and to medical research n(A∩B) = 32

Number of graduates donated to medical research and to preserve the environment n(B∩C) = 48

Number of graduates  donated to a political campaign and to preserve the environment n(C∩A) = 56

Now,

n(U)=n(A)+n(B)+n(C)-n(A∩B)-n(B∩C) -n(C∩A)+n(A∩B∩C)+n(none)

$n(U)=91+76+131-32-48-56+27+24=213$

So, What percent of the college graduates donated to none of the three listed causes?

Percentage would be

$\dfrac{24}{213}\times 100\\\\=11.26\%$

(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)=107

Percentage would be

$\dfrac{107}{213}\times 100\\\\=50.23\%$

Hence, a) 11.26% and b) 50.23%