Question

n a certain year, 88% of all Caucasians in the U.S., 73% of all African-Americans, 73% of all Hispanics, and 74% of residents not classified into one of these groups used the Internet for e-mail. At that time, the U.S. population was 65% Caucasian, 12% African-American, and 13% 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

P(Caucasian) = 0.65

P(African American) = 0.12

P(Hispanic) = 0.13

P(Others) = 1 - (0.65 + 0.12 + 0.13) = 0.10

Bayes' Theorem: P(A | B) = P(A & B) / P(B)

P(Hispanic | used the internet for e-mail) = P(Hispanic and used the internet for e-mail) / P(used the internet for e-mail)

= P(Hispanic and used the internet for e-mail) / [P(Caucasian and used the internet for e-mail) + P(African-American and used the internet for e-mail) + P(Hispanic and used the internet for e-mail) + P(Others and used the internet for e-mail)]

= (0.13x0.73)/(0.65x0.88 + 0.12x0.73 + 0.13x0.73 + 0.10x0.74)

= 0.11

= 11%