A company produces 10,000 items per day. On a | vedclass

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

Question

(C) Let $E$ be the event that the selected item is defective. Let $A, B, C$ be the events that the item was produced by machines $A, B, C$ respectivel

Vedclass · Accepted Answer

$\frac{40}{71}$

Vedclass · Answer

(C) Let $E$ be the event that the selected item is defective. Let $A, B, C$ be the events that the item was produced by machines $A, B, C$ respectively.Given probabilities:$P(A) = \frac{2500}{10000} = 0.25$$P(B) = \frac{3500}{10000} = 0.35$$P(C) = \frac{4000}{10000} = 0.40$Conditional probabilities of defect:$P(E|A) = \frac{2}{100} = 0.02$$P(E|B) = \frac{3}{100} = 0.03$$P(E|C) = \frac{5}{100} = 0.05$Using Bayes' theorem, the probability that the item was produced by machine $C$ given it is defective is:$P(C|E) = \frac{P(E|C) \cdot P(C)}{P(E|A) \cdot P(A) + P(E|B) \cdot P(B) + P(E|C) \cdot P(C)}$$P(C|E) = \frac{0.05 \cdot 0.40}{(0.02 \cdot 0.25) + (0.03 \cdot 0.35) + (0.05 \cdot 0.40)}$$P(C|E) = \frac{0.0200}{0.0050 + 0.0105 + 0.0200} = \frac{0.0200}{0.0355} = \frac{200}{355} = \frac{40}{71}$

Similar Questions

In an entrance test,there are multiple-choice questions. There are four possible answers to each question,of which one is correct. The probability that a student knows the answer to a question is $9/10$. If he gets the correct answer to a question,then the probability that he was guessing is:

Two digits are selected at random from the digits $1$ through $9$. If their sum is even,then the probability that both are odd is

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module