Question: A soft drink bottling company maintains records concerning the number of unacceptable bottles of soft drink for the filling and capping machines. Based on past data, the probability that a bottle came from machine I and was nonconforming is 0.01, and the probability that a bottle came from machine II and was nonconforming is 0.005. Half the bottles are filled on machine I. The other half is filled on machine II. If a filled bottle of soft drink is randomly selected, what is the probability that

a. It is a nonconforming bottle?

b. It was filled on machine I and is a conforming bottle?

c. It was filled on machine I or is a conforming bottle?

d. Suppose you know that the bottle was filled on machine I. What is the probability that it is nonconforming?

e. Suppose you know that the bottle is nonconforming. What is the probability that it was filled on machine I?

f. Explain the difference in the answers to (d) and (e). (Hint: Construct a 2 x 2 contingency table to evaluate the probabilities.)