It has generally been believed that it is not feasible for men and women to be just friends (The New York Times, April 12, 2012). Others argue that this belief may not be true anymore since gone are the days when men worked and women stayed at home and the only way they could get together was for romance. In a recent survey, 186 heterosexual college students were asked if it was feasible for men and women to be just friends. Thirty-two percent of females and 57% of males reported that it was not feasible for men and women to be just friends. Suppose the study consisted of 100 female and 86 male students.
a. Construct a contingency table that shows frequencies for the qualitative variables Gender (men or women) and Feasible (yes or no).
b. Find the probability that a student believes that men and women can be friends.
c. If a student believes that men and women can be friends, what is the probability that this student is a male? Find the corresponding probability that this student is a female.