Do people of different age groups differ in their response to email messages? A survey by the Center for the Digital Future of the University of Southern California (data extracted from A. Mindlin, "Older E-mail Users Favor Fast Replies," The New York Times, July 14, 2008, p. B3) reported that 70.7% of users over 70 years of age believe that email messages should be answered quickly, as compared to 53.6% of users 12 to 50 years old. Suppose that the survey was based on 1,000 users over 70 years of age and 1,000 users 12 to 50 years old. The following table summarizes the results:

a. Suppose you know that the respondent is between 12 and 50 years old. What is the probability that he or she answers quickly?
b. Suppose you know that the respondent is over 70 years old. What is the probability that he or she answers quickly?
c. Are the two events, answers quickly and age of respondents, independent? Explain.

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ANSWERS QUICKLY AGE OF RESPONDENTS 12-50 Over 70 Total 707 1,243 757 1,000 ,000 2,000 Yes No Total 536 464 0 293