SOLUTION: An electronic toy manufacturer uses a particular kind of quality test to check the toys. The test indicates defects in 85% of defective toys, but it also indicates defects in 2% o

Question 81424: An electronic toy manufacturer uses a particular kind of quality test to check the toys. The test indicates defects in 85% of defective toys, but it also indicates defects in 2% of nondefective toys. The test indicates that toy A is defective. If 5% of toys have defects, what is the probability that toy A has a defect?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
An electronic toy manufacturer uses a particular kind of quality test to check the toys. The test indicates defects in 85% of defective toys, but it also indicates defects in 2% of nondefective toys. The test indicates that toy A is defective. If 5% of toys have defects, what is the probability that toy A has a defect?
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Let D be defective and D' be non defective:
The Problem is a Bayes problem.
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P(D) = P(D and D) + P(D and D')
=P(D)*P(D|D) + P(D)*P(D|D')
=P(D)[P(D|D)+P(D|D')]
=0.05[0.85+P(D|D')]
Need to find P(D|D')
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P(D|D') = [P(D and D')/P(D')] = [P(D'|D)P(D)/P(D')] = [0.02*0.05/0.95]=0.0010526...
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Put that is the P(D) line up above to get:
P(D)=0.05[0.85+0.0010526]= 0.05(0.8510526)=0.0426
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P(a randomly selected item is defective is defective )= 0.0426
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Cheers,
Stan H.
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