Question

. Consider the following table which shows soft drink preferences in different age groups. Under 21 21-40 Over 40 Cola Root Beer 15 25 2012 Lemon-Lime 10 38 16 14 20 a. If one of the 150 subjects is randomly selected, find the probability that they drink root beer given that they are under 21. b. If one of the 150 subjects is randomly selected, find the probability that they drink cola or are over 40. C. If one of the 150 subjects is randomly selected, find the probability that they do not drink cola given that they are in the 21-40 age range.

Answer 1

Total students = 150

a) P(drink root beer | under 21) = P(drink root beer and under 21) / P(under 21)

                                                  = (25/150) / ((15 + 25 + 10)/150)

                                                  = 25 / 50

                                                  = 1/2

b) P(drink cola or over 40) = P(drink cola) + P(over 40) - P(drink cola and over 40)

                                           = (15 + 20 + 14)/150 + (14 + 20 + 16)/150 - 14/150

                                           = 85/150

                                           = 17/30

c) P(do not drink cola | 21-40 age) = 1 - P(drink cola | 21-40 age)

                                                       = 1 - (P(drink cola And 21-40 age) / P(21-40 age) )

                                                       = 1 - ((20/150) / ((20 + 12 + 38)/150))

                                                       = 1 - 20/70

                                                       = 5/7