Question 1023994: A restaurant chain routinely surveys customers andamong other questions asks each customer whether he or she wouldreturn and to rate the quality of food. Summarizing hundreds ofthousands of questionnaires produced this table of jointprobabilities?
Rating Customer WillReturn Customer Will NotReturn
Poor 0.02 0.1
Fair 0.08 0.09
Good 0.35 0.14
Excellent 0.2 0.02
a. What proportion of customers say that they will return andrate the restaurant's food as good?
b. What proportion of customers who say that they will returnrate the restaurant's food as good?
c. What proportion of customers who rate the restaurant's foodas good say that they will return?
d. Discuss the differences in your answers to Parts a, b,c.
Answer by robertb(5830)   (Show Source):
You can put this solution on YOUR website! a. 0.35, or 35%
b. 0.65, or 65% of the customers say they will return. Of this, 0.35 or 35% say it's good. So the proportion is 0.35/0.65 = 7/13, or 53.85%
c. 0.49, or 49% of the customers say it is good. Of this, 0.35 or 35% they will return. So the proportion is 0.35/0.49 = 5/7, or 71.42%.
d. Part a is simply joint probability, whereas b and c are conditional probabilities, and require evaluation of marginal probabilities.
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