4. A well known apple juice production company maintains records concerning the

Question

4. A well known apple juice production company maintains records concerning the number of unacceptable containers of apple juice obtained from the filling and capping machines. Based on past data, the probability that a container came from machine I and was nonconforming is 0.03 and the probability that a container came from machine II and was nonconforming is 0.02. These probabilities represent the probability of one container out of the total sample having the specified characteristics. Half the containers are filled on machine I and the other half are filled on machine II. a. If a filled container of juice is selected at random, what is the probability that it is an acceptable container? b. If a filled container of juice is selected at random, what is the probability that it was filled on machine II? c. If a filled container of juice is selected at random, what is the probability that it was filled on machine I and is an acceptable container?

Explanation / Answer

First prepare a table of the given data:

Prob for acceptable container = 1-(0.0150+0.0100) = 0.975

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b) For machine II prob =0.50

c) Prob (machine A and acceptable) = 0.50(1-0.03) = 0.485

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