In a toy factory,machines A, B,and C are used | vedclass

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(D) Let $E$ be the event that the toy is defective. Let $A, B, C$ be the events that the toy is manufactured by machines $A, B, C$ respectively.Given

Vedclass · Accepted Answer

$4 / 7$

Vedclass · Answer

(D) Let $E$ be the event that the toy is defective. Let $A, B, C$ be the events that the toy is manufactured by machines $A, B, C$ respectively.Given probabilities:$P(A) = \frac{30}{100}, P(B) = \frac{40}{100}, P(C) = \frac{30}{100}$$P(E|A) = \frac{2}{100}, P(E|B) = \frac{3}{100}, P(E|C) = \frac{1}{100}$Using Bayes' theorem,the probability that the defective toy was manufactured by machine $B$ is:$P(B|E) = \frac{P(B) 	imes P(E|B)}{P(A) 	imes P(E|A) + P(B) 	imes P(E|B) + P(C) 	imes P(E|C)}$$P(B|E) = \frac{\frac{40}{100} 	imes \frac{3}{100}}{\frac{30}{100} 	imes \frac{2}{100} + \frac{40}{100} 	imes \frac{3}{100} + \frac{30}{100} 	imes \frac{1}{100}}$$P(B|E) = \frac{120}{60 + 120 + 30} = \frac{120}{210} = \frac{4}{7}$

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