Mathematics - Bayes Formula Jim Orson’s factory obtains capacitors from three different partners: 40% from A,...
Mathematics - Bayes Formula
Jim Orson’s factory obtains capacitors from three different partners: 40% from A, 10% from B, and 50% from C.
The defective rates for these partners are 3%, 3%, and 4% respectively.
If a defective capacitor is returned, what is the probability that it came from partner A? From B? From C?
Homework Answers
P(Defective) =P(A)*P(defective|A)+P(B)*P(defective|B)+P(C)*P(defective|C)
=0.4*0.03+0.1*0.03+0.5*0.04 =0.035
therefore posterior probability if a defective is found"
P(A|defective )=P(A)*P(defective|A)/P(Defective) =0.4*0.03/0.035=0.3429
P(B|defective )=P(B)*P(defective|A)/P(Defective) =0.1*0.03/0.035=0.0857
P(C|defective )=P(C)*P(defective|A)/P(Defective) =0.5*0.04/0.035=0.5714
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Mathematics - Bayes Formula
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