Question

In a certain year, 86% of all Caucasians in the U.S., 74% of all African-Americans, 74% of all Hispanics, and 80% of residents not classified into one of these groups used the Internet for e-mail. At that time, the U.S. population was 69% Caucasian, 12% African-American, and 11% Hispanic. What percentage of U.S. residents who used the Internet for e-mail were Hispanic? (Round your answer to the nearest whole percent.)

Answer 1

let C = Caucasians

A = African-Americans

H = Hispanics

O = not Classified

I = internet user

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P(I|C) = 0.86

P(I|A) = 0.74

P(I|H) = 0.74

P(I|O) = 0.80

P(C) = 0.69

P(A) = 0.12

P(H) = 0.11

P(O) = 1-0.69-0.12-0.11 = 0.08

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percentage of U.S. residents who used the Internet for e-mail were Hispanic, P(H|I) =

= (P(I|H)*P(H)) / (P(I|C)*P(C) + P(I|A)*P(A) +P(I|H)*P(H) +P(I|O)*P(O) )

= (0.74*0.11) / (0.86*0.69 + 0.74*0.12 + 0.74*0.11 + 0.80*0.08)

= 0.098 = 0.1= 10%