In an automated filling operation, the probability of an

Chapter 2, Problem 211SE

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QUESTION:

Problem 211SE

In an automated filling operation, the probability of an incorrect fill when the process is operated at a low speed is 0.001. When the process is operated at a high speed, the probability of an incorrect fill is 0.01. Assume that 30% of the containers are filled when the process is operated at a high speed and the remainder are filled when the process is operated at a low speed.

(a) What is the probability of an incorrectly filled container?

(b) If an incorrectly filled container is found, what is the probability that it was filled during the high-speed operation?

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QUESTION:

Problem 211SE

In an automated filling operation, the probability of an incorrect fill when the process is operated at a low speed is 0.001. When the process is operated at a high speed, the probability of an incorrect fill is 0.01. Assume that 30% of the containers are filled when the process is operated at a high speed and the remainder are filled when the process is operated at a low speed.

(a) What is the probability of an incorrectly filled container?

(b) If an incorrectly filled container is found, what is the probability that it was filled during the high-speed operation?

ANSWER:

Solution:

Step 1 of 3:

From the given problem,

     Let us denote the event A is incorrectly filled container

                             Event B is process is operated at low speed

                             Event  is process is operated at high speed.

                    The probabilities are

                     

                     

                     


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