In a certain year, 88% of all Caucasians in the U.S., 75% of all African-Americans, 75% of all Hispanics, and 82% of residents not classified into one of these groups used the Internet for e-mail. At that time, the U.S. population was 64% Caucasian, 10%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.) Use Bayes’ theorem or a tree diagram to calculate the indicated probability. Round your answer to four decimal places. HINT [See Example 3.]Y1, Y2, Y3 form a partition of S. P(X | Y1) = .3, P(X | Y2) = .1, P(X | Y3) = .6, P(Y1) = .6, P(Y2) = .2. Find P(Y1 | X).
In a certain year, 88% of all Caucasians
in the U.S., 75% of all African-Americans, 75% of all Hispanics, and 82% of residents not classified into one of these groups used the Internet for e-mail. At that time, the U.S. population was 64% Caucasian, 10%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.)
Use Bayes’ theorem or a tree diagram to calculate the indicated probability. Round your answer to four decimal places. HINT [See Example 3.]Y1, Y2, Y3 form a partition of S. P(X | Y1) = .3, P(X | Y2) = .1, P(X | Y3) = .6, P(Y1) = .6, P(Y2) = .2.
Find P(Y1 | X).
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