A company manufactures transistors in four factories producing 10%, 30%, 40% and 20% of the parts respectively. Due to their respective age and level of standards, factories produce defective parts at frequencies different, i.e. 0.15, 0.20, 0.08 and 0.10. If we take a part at random from among those that are defective, what is the probability that it comes from factory 3?
A company manufactures transistors in four factories producing 10%, 30%, 40% and 20% of the parts respectively. Due to their respective age and level of standards, factories produce defective parts at frequencies different, i.e. 0.15, 0.20, 0.08 and 0.10. If we take a part at random from among those that are defective, what is the probability that it comes from factory 3?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Question
A company manufactures transistors in four factories producing 10%, 30%, 40% and 20% of the parts respectively.
Due to their respective age and level of standards, factories produce defective parts at frequencies
different, i.e. 0.15, 0.20, 0.08 and 0.10.
If we take a part at random from among those that are defective, what is the
Expert Solution
Step 1: Introduce the given information
According to the given information ,
P(factory 1) = P(f1) = 0.10
P(factory 2) = P(f2) = 0.30
P(factory 3) = P(f3)=0.40
P(factory 4) = P(f4)= 0.20
Let D denote the factories produce defective parts .
P(D | factory 1) = 0.15
P( D | factory 2) = 0.20
P(D | factory 3) = 0.08
P(D | factory 4) = 0.10
Using Formula ,
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