Pop soda and coke are three terms that arc used to refer to

\'\'Pop,\'\' \'\'soda,\'\' and \'\'coke\'\' are three terms that arc used to refer to carbonated soda drinks. The frequency each is used varies across the United Slates according to the table that follows. At a large university, 4%, 10%, 6%, 18%, 28%, and 34% of the students are from the Pacific, Rocky Mountains, Southwest, Midwest, Northeast, and Southeast, respectively. a What is the probability that a randomly selected student from this university is from the Pacific region and uses the term \'\'soda\'\'? b What is the probability that a randomly selected student from this university uses \'\'pop\'\' when referring to carbonated beverages? c A student is selected al random from among the students who use the term \'\'coke.\'\' What is the probability that she or he is from the Southeast?

Solution

a)

P(Pacific and soda) = P(Pacific) P(Soda|Pacific) = 0.04(0.71)

= 0.0284 [answer]

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b)

P(Pop) = Sum [P(place) P(Pop|Place)] = 0.04(0.15) + 0.10(0.61) + 0.06(0.12) + 0.18(0.70) + 0.28(0.30) + 0.34(0.18)

= 0.3454 [answer]

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c)

P(Southeast|Coke) = [P(Southeast) P(Coke|Southeast)] / Sum [P(place) P(Coke|place)]

= [0.34(0.39)] / [0.04(0.14) + 0.10(0.08) + 0.06(0.65) + 0.18(0.04) + 0.28(0.02) + 0.34(0.39)]

= 0.669696969 [answer]