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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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}$

Similar Questions

$A$ bag contains $2n+1$ coins. It is known that $n$ of these coins have a head on both sides, whereas the remaining $n+1$ coins are fair. $A$ coin is picked up at random from the bag and tossed. If the probability that the toss results in a head is $\frac{31}{42}$, then $n$ is equal to

Bag $A$ contains $3$ white and $7$ red balls,and bag $B$ contains $3$ white and $2$ red balls. One bag is selected at random and a ball is drawn from it. What is the probability that the ball was drawn from bag $A$,given that the ball drawn is white?

In four schools $B_1, B_2, B_3, B_4$,the percentage of girl students is $12, 20, 13, 17$ respectively. From a school selected at random,one student is picked up at random and it is found that the student is a girl. The probability that the school selected is $B_2$ is:

$A$ man is known to speak truth $3$ out of $4$ times. He throws a die and reports that it is a six. Find the probability that it is actually a six.

Vedclass Test Series

Exam Paper Generator

Online Exam Module