A restaurant chain routinely surveys its customers.

Among other questions, the survey asks each customer whether he or she would return and to rate the quality of food. Summarizing hundreds of thousands of questionnaires produced this table of joint probabilities.

Customer Customer Will Rating Will Return Not Return Poor .02 .10 Fair .08 .09 Good .35 .14 Excellent .20 .02

a. What proportion of customers say that they will return and rate the restaurant’s food as good?

b. What proportion of customers who say that they will return rate the restaurant’s food as good?

c. What proportion of customers who rate the restaurant’s food as good say that they will return?

d. Discuss the differences in your answers to parts

(a), (b), and (c).