SOLUTION: 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 proba

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Question 1132800: 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 by ikleyn(52855) About Me  (Show Source):
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(a)   what is the probability of an incorrectly filled container? 

      0.3*0.01 + (1-0.3)*0.001 = 0.0037 = 0.37%.


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

     %280.3%2A0.01%29%2F%280.3%2A0.01+%2B+0.7%2A0.001%29 = 0.81081 = 81.81%.


The formulas are self-explanatory.