A company has two plants A and B to manufactu | vedclass

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

Question

(A) Let $E_1$ be the event that the motorcycle is manufactured at plant $A$,and $E_2$ be the event that it is manufactured at plant $B$. Let $S$ be th

Vedclass · Accepted Answer

$54$

Vedclass · Answer

(A) Let $E_1$ be the event that the motorcycle is manufactured at plant $A$,and $E_2$ be the event that it is manufactured at plant $B$. Let $S$ be the event that the motorcycle is of standard quality.Given:$P(E_1) = 0.60$$P(E_2) = 0.40$$P(S|E_1) = 0.80$$P(S|E_2) = 0.90$Using Bayes' Theorem,the probability $p$ that the motorcycle was manufactured at plant $B$ given it is of standard quality is:$p = P(E_2|S) = \frac{P(S|E_2)P(E_2)}{P(S|E_1)P(E_1) + P(S|E_2)P(E_2)}$Substituting the values:$p = \frac{0.90 	imes 0.40}{(0.80 	imes 0.60) + (0.90 	imes 0.40)}$$p = \frac{0.36}{0.48 + 0.36} = \frac{0.36}{0.84} = \frac{36}{84} = \frac{3}{7}$We need to find $126p$:$126p = 126 	imes \frac{3}{7} = 18 	imes 3 = 54$Thus,the value is $54$.

Similar Questions

Three similar urns $A, B, C$ contain $2$ red and $3$ white balls; $3$ red and $2$ white balls; $1$ red and $4$ white balls respectively. If a ball selected at random from one of the urns is found to be red, then the probability that it is drawn from urn $C$ is

$A$ man speaks truth $2$ out of $3$ times. He picks one of the natural numbers in the set $S=\{1, 2, 3, 4, 5, 6, 7\}$ and reports that it is even. The probability that it is actually even is

Events $E_{1}$ and $E_{2}$ form a partition of the sample space $S$. $A$ is any event such that $P(E_{1}) = P(E_{2}) = \frac{1}{2}$,$P(E_{2} | A) = \frac{1}{2}$,and $P(A | E_{2}) = \frac{2}{3}$. Then $P(E_{1} | A)$ is:

Bag $A$ contains $2$ white and $3$ red balls. Bag $B$ contains $4$ white and $5$ red balls. One bag is chosen at random and a ball is drawn from it,which is found to be red. Find the probability that it was drawn from bag $B$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module