# Probability: Probability Theorems – #60

Question: A soft drink bottling company maintains records concerning the number of unacceptable bottles of soft drink obtained from the filling and capping machines. Based on past data, the probability that a bottle came from machine I and was nonconforming is 0.05 and the probability that a bottle came from machine II and was nonconforming is 0.025. These probabilities are representing the probability of one bottle out of the total sample having the specified characteristics. Half the bottles are filled on machine I and the other half are filled on machine II.

a. Give an example of a simple event.

b. Give an example of a joint event.

c. If a filled bottle of soft drink is selected at random, what is the probability that it is a nonconforming bottle?

d. If a filled bottle of soft drink is selected at random, what is the probability that it was filled on machine II?

e. If a filled bottle of soft drink is selected at random, what is the probability that it was filled on machine I and is a conforming bottle?