LEC06 Bayes

# LEC06 Bayes - Bayes Theorem A supplies 60 of parts with...

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Bayes' Theorem A supplies 60% of parts with fraction defective 0.02. B supplies 40% of parts with fraction defective 0.05. events event D = part is defective event A = part comes from supplier A event B = part comes from supplier B Given P(A) =.6 P(D/A)=.02 P(B) =.4 P(D/B)=.05 A D B

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Find the Probability a unit is defective. P D P D A P A P D B P B ( ) ( / ) ( ) ( / ) ( ) = + =(.02)(.6) + (.05)(.4) = .012 + .020 = .032 Given the unit is defective, find the probability it came from supplier A P A D P A D P D P D A P A P D ( / ) ( ) ( ) ( / ) ( ) ( ) . (. ) . . = = = = 02 6 032 375 2
Supplier % of supply fraction def. 1 20 .05 2 30 .04 3 10 .02 4 40 .01 Find the probability of a defective P D P D B P B P D B P B P D B P B P D B P B ( ) ( / ) ( ) ( / ) ( ) ( / ) ( ) ( / ) ( ) . (. ) . (. ) . (. ) . (. ) . . . . . = + + + = + + + = + + + = 1 1 2 2 3 3 4 4 05 20 04 30 10 02 40 01 01 012 002 004 028 Find P(B 2 / D) P B D P B D P D P D B P B

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LEC06 Bayes - Bayes Theorem A supplies 60 of parts with...

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