Answer to Question #119447 in Statistics and Probability for desmond

Question

In a bolt manufacturing factory, machines A; B; and C produce 25%, 30% and 45%
of the total output, respectively. Of their outputs, 7%; 6% and 4% are defective bolts,
respectively. If a bolt drawn at random from the production is found to be defective,
what is the probability that it was manufactured by machine C?

Answer 1

P=(P(C).P(defective∣С))/((P(A).P(defective∣A)+(P(B).P(defective∣B)+(P(C).P(defective∣С))

P(A)=25/100=0.25

P(B)=30/100=0.3

P(C)=45/100=0.45

P(defective∣A)=7/100=0.07

P(defective∣B)=6/100=0.06

P(defective∣С)=4/100=0.04

P=(0.45*0.04)/( 0.25*0.07+0.3*0.06+0.45*0.04)=0.018/0.0535=0.336