The accompanying table gives information on the type of coffee selected by someo

Question

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 24% 20% 16% Decaf 20% 10% 10% 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.) What is the probability that the individual purchased a cup of decaf coffee? (Enter your answer to two decimal places.) (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.) How would you interpret this probability? This is the probability of people who choose aSelec- 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.) cup, given that they chose a Select cup of coffee (c) How does this compare to the corresponding unconditional probability of (a)? This probability is-Select- the unconditional probability of selecting a small size.

Explanation / Answer

a)
P(Small cup) = 0.24 + 0.2 = 0.44

P(Decaf coffee) = 0.2 + 0.1 + 0.1 = 0.4

b)
P(Decaf | Small) = P(Decaf and Small)/P(Small)
= 0.2/0.44 = 0.4545

This is the probability of people who choose a Decaf cup, given that the chose a small cup of coffee.

c)
P(Small | Decaf) = P(Decaf and Small)/P(Decaf)
= 0.2/0.4 = 0.5

This probability is greater than the unconditional probability of selecting a small size.

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