Question Solved1 Answer In a factory, machines A, B, and C manufacture 20%, 45%, and 35% of the total production of bolts, respectively. Of the bolts manufactured by the machine A, B, and C, 4%, 2% and 3% are defective, respectively. A bolt is drawn at random and is found to be defective. What is the probability that it was produced by C? [6 points)

IBWYYZ The Asker · Advanced Mathematics

Transcribed Image Text: In a factory, machines A, B, and C manufacture 20%, 45%, and 35% of the total production of bolts, respectively. Of the bolts manufactured by the machine A, B, and C, 4%, 2% and 3% are defective, respectively. A bolt is drawn at random and is found to be defective. What is the probability that it was produced by C? [6 points)
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Transcribed Image Text: In a factory, machines A, B, and C manufacture 20%, 45%, and 35% of the total production of bolts, respectively. Of the bolts manufactured by the machine A, B, and C, 4%, 2% and 3% are defective, respectively. A bolt is drawn at random and is found to be defective. What is the probability that it was produced by C? [6 points)
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A : bolt manufactured by AB: bolt manufactured by BC : bolt manufactured by CD: bolt is defectived.we need to find the probability that the bolt is defective and is manufactured by ' C '.P(C//D)=(P(C)*P(D//C))/(P(A)P(D//A)+P(B)P(P//B)+P(C)PP//C))rarr(1)P(A)rarr probability that the bolt is made by A.P(A)=20%=>(2theta)/(100)=0.20=>P(A)=0.20P(B)rarr probability that the bolt is made by BP(B)=45%=>(45)/(100)=0.45=>P(B)=0.45P(C)rarr probability that the ... See the full answer