The accompanying table gives information on the type of coffee selected by someone purchasing a single cup at a particular airport kiosk. Consider randomly selecting such a coffee purchaser. a. ?What is the probability that the individual purchased a small cup? A cup of decaf coffee? b. ?If we learn that the selected individual purchased a small cup, what now is the probability that he/she chose decaf coffee, and how would you interpret this probability? c?. ?If we learn that the selected individual purchased decaf, what now is the probability that a small size was selected, and how does this compare to the corresponding unconditional probability of (a)?

Answer : Step 1 of 3 : Given, The accompanying table gives information on the type of coffee selected by someone purchasing a single cup at a particular airport kiosk. Small Medium Large Regular 14% 20% 26% Decaf 20% 10% 10% a) the probability that the individual purchased a small cup A cup of decaf coffee P(individual purchase a small cup) = 0.14 + 0.20 = 0.34 P(decaf) = 0.20 + 0.10 + 0.10 = = 0.40 Step 2 of 3 : b) if the selected individual purchased a small cup P(decaf coffee/small cup) =(decaf coffee small cup) P(Small cup) 0.20 = 0.34 = 0.588 Here the sample space is reduced to people who purchase small cup of coffee.