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?

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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?

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 ,

P open parentheses A vertical line B close parentheses equals fraction numerator P open parentheses B vertical line A close parentheses cross times P left parenthesis A right parenthesis over denominator P left parenthesis B right parenthesis end fraction

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