An apple juice bottling company maintains records concerning the number of unacceptable bottles of juice obtained from the filling and capping machines. Based on past data, the joint probability that a bottle came from machine I and was nonconforming is 0.05 and the joint probability that a bottle came from machine II and was nonconforming is 0.075. These probabilities represent the probability of one bottle out of the total sample having the specified characteristics. Half of the bottles were filled on machine I and the other half were filled on machine II.
Compute: a. If a filled bottle is selected at random, what is the probability that it is a nonconforming bottle? b. If a filled bottle is selected at random, what is the probability that it was filled on machine II? c. If a filled bottle is selected at random, what is the probability that it was filled on machine I and is a conforming bottle?