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. Consider randomly selecting such a coffee purchaser. What is the probability that the individual purchased a small cup? 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 part a?

Explanation / Answer

Part-A

P(Individual purchased a small cap)=0.15+0.19 =0.34

Part-B

P(Chose decaf coffee/small cap) =P(Chose decaf coffee and small cap)/P(Small cap)

=0.19/0.34

=0.56

We interpret this as there is 56% chance that who chose small cap will also choose decaf coffee

Part-C

P(Small Cap/ Decaf)= P(Small cap and Decaf)/P(Decaf)

=0.19/(0.19+0.11+0.11)

=0.46

This means that those who chose dcafe are 46% likely to chose small cap.

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