Assume there are three machines A, B, and C in |a manufacturing facility that ma

Question

Assume there are three machines A, B, and C in |a manufacturing facility that makes an iPhone component. They manufacture, respectively, 40, 30, and 30 percent of the total iPhone components there. Of their outputs, respectively, 2, 3, and 4 percent of the components are defective. A component is drawn randomly from the combined output of the three machines, what is the probability that it will be defective? Given that the component is defective, what is the probability that it is made by machine A?

Explanation / Answer

let probability of from A =P(A)=40/100=0.4

from B=P(B)=30/100=0.3

and from C=P(C)=0.3

also probabilty of defective =P(D)

a)probabilty of defective =P(D)=P(A)*P(D|A)+P(B)*P(D|B)+P(C)*P(D|A) =0.4*0.02+0.3*0.03+0.3*0.04=0.029

b) probabilty that it is made by m/c A , given defective =P(A|D) =P(A)*P(D|A)/P(D) =0.4*0.02/0.029=0.2759

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