9. Eighty students in a school cafeteria were asked if they favored a ban on smo
ID: 3358934 • Letter: 9
Question
9. Eighty students in a school cafeteria were asked if they favored a ban on smoking in the cafeteria. The results of the survey are shown in the table Class Freshman Sophomore Oppose No opinion 27 15 23 If a student is selected at random, find these probabilities (a) The student is a freshman. (b) The student is a freshman and favors the ban. (c) The student is a freshman or favors the ban. (d) Given that the student favors the ban, the student is a sophomore. (e) The student has no opinion about the ban, given that the student is a freshman.Explanation / Answer
Total number of students = 80
(a) P(freshman) = 50/80 = 0.625
(b) P(freshman and favors ban) = 15/80 = 0.1875
(c) P(freshman or favors ban) = P(freshman) + P(favors ban) - P(freshman and favors ban)
= 0.625+ 0.475 - 0.1875 = 0.9125
(d) P(sophomore given that student favor ban) = P(favor ban and sophomore)/P(favors ban)
= (23/80)/ (38/80) = 0.6053
(e) P(no opinion given that student is freshman) = P(no opinion and freshman)/P(freshman)
= 0.1/0.625 = 0.16
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