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In an automated filling operation, the probability of an
Chapter 2, Problem 211SE(choose chapter or problem)
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?
Questions & Answers
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