4) Suppose that you are at a coffee tasting convention and you walk up to a stan

Question

4) Suppose that you are at a coffee tasting convention and you walk up to a stand that is sampling three different coffee drinks: Cappuccino, Espresso, and Turkish Coffee. The vendor tells you that there are 10 samples of Cappuccino on the table, 5 samples of Espresso, and 5 samples of Turkish coffee, but being unfamiliar with coffee, you cannot tell which is which on the table. Also on the table is a list of reviews about the three different coffees from the previous years convention, labeling the percentage of people that thought the coffee tasted good, okay, or bad. Suppose you randomly select a coffee on the table to sample TABLE 1. Ratings Cappuccino | 40% | 40% 20% Espresso | 20% | 50% | 30% Turkish | 80% | 5% | 15% (a) (10 points) What is the probability that the coffee you selected does not taste good? (b) (10 points) If the coffee tastes good, what is the probability that it is Turkish coffee?

Explanation / Answer

a)P(Coffee does not tate good)=P(Cappucion and does not taste good+Espresso and does not taste good+Turkish and does not taste good) =(10/20)*(0.4+0.2)+(5/20)*(0.5+0.3)+(5/20)*(0.05+0.15)=0.55

b)P(coffee taste good) =1-P(coffee does not taste good) =1-0.55 =0.45

hence P(Turkish cofffee|taste good) =P(Turkish)*P(taste good|turkish)/P(taste good)

=(5/20)*0.8/0.45=0.4444

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