Question

In a recent survey of monetary donations made by 489 college graduates, the following information was obtained. 95 has donated to a political campaign, 76 had donated to assist medical research, 133 had donated to preserve the environment, 25 had donated to all three, 38 had donated to a political campaign and to medical research, 46 had donated to medical research and to preserve the environment, and 54 donated to a political campaign and to preserve the environment.

(a) How many college graduates donated to none of the listed causes?
(b) What percent of the college graduates donated to exactly one of the three listed causes?

Answer 1

Explanation:

The Venn diagram representing this situation is shown in the attached photo.

P represents the set of college graduates that donated to a political campaign.

M represents the set of college graduates that donated to assist medical research.

E represents the set of college graduates that donated to preserve the environment.

From the diagram,

The number of college graduates that donated to all three is 25

The number of college graduates that donated to a political campaign and medical research only is

38 - 25 = 13

The number of college graduates that donated to a political campaign and preserve the environment only is

54 - 25 = 29

The number of college graduates that donated to medical research and to preserve the environment only is 46 - 25 = 21

The number of college graduates that donated to a political campaign only is

95 - (29 + 25 + 13) = 28

The number of college graduates that donated to medical research only is

76 - (13 + 25 + 21) = 17

The number of college graduates that donated to preserve the environment only is

133 - (29 + 25 + 21) = 58

a) the number of college graduates that donated to none is

489 - (28 + 17 + 58 + 13 + 21 + 29 + 25)

= 298 college graduates

b) the number of college graduates that donated to exactly one of the three listed causes is

28 + 17 + 58 = 103

The percentage would be

103/489 × 100 = 21.1%