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 12% 24% 16% Decaf 24% 12% 12% Consider randomly selecting such a coffee purchaser. (a) What is the probability that the individual purchased a small cup? (Enter your answer to two decimal places.) [:J What is the probability that the Individual purchased a cup of decaf coffee? (Enter your answer to two decimal places.) H (b) If we learn that the selected individual purchased a small cup, what now is the probability that he/she chose decaf coffee? {Round your answer to three decimal places.) :1 How would you interpret this probability? This Is the probability of people who choose a -Select--- 0 cup, given that they chose a -Seleot- 0 cup of coffee. (c) If we learn that the selected individual purchased decaf, what now Is the probability that a small size was selected? (Enter your answer to one decimal place.) [2 How does this compare to the corresponding unconditional probability of (a)? This probability is Select 3 the unconditional probability of selecting a small size. Need Help? 12. [-12 Points] DETAILS DEVORESTATS 2.4.062. MY NOTES ASK YOUR TEACHER Blue Cab operates 15% of the taxis in a certain city, and Green Cab operates the other 85%. After a nighttime hit-and-run accident involving a taxi, an eyewitness said the vehicle was blue. Suppose, though, that under night vision conditions, only 80% of individuals can correctly distinguish between a blue and a green vehicle. What is the (posterior) probability that the taxi at fault was blue? [ii-flint: A tree diagram might help. Note: This is based on an actual incident] (Round your answer to four decimal places.) [:1 Indicate the probability rule you used. 0 The Product Rule for Ordered Pairs O The Division Rule 0 Bayes' Theorem 0 The Product Rule far k-Tuples O The Rule of Permutations Need Help