A factory has a total of three manufacturing | vedclass

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

Question

(C) Let the total number of bulbs produced be $100$. Since the production ratio is $2:2:1$,the number of bulbs produced by $M_1, M_2$,and $M_3$ are $4

Vedclass · Accepted Answer

$0.30$

Vedclass · Answer

(C) Let the total number of bulbs produced be $100$. Since the production ratio is $2:2:1$,the number of bulbs produced by $M_1, M_2$,and $M_3$ are $40, 40$,and $20$ respectively.Given that $20\%$ of total bulbs are defective,total defective bulbs $= 20$.For $M_1$,$15\%$ of $40$ bulbs are defective,so $0.15 	imes 40 = 6$ bulbs are defective.Let $x$ be the number of defective bulbs produced by $M_3$. Then the number of defective bulbs produced by $M_2$ is $20 - 6 - x = 14 - x$.Given that the probability that a randomly chosen defective bulb was produced by $M_2$ is $\frac{2}{5}$,we have:$P(M_2 | 	ext{Defective}) = \frac{	ext{Defective bulbs from } M_2}{	ext{Total defective bulbs}} = \frac{14 - x}{20} = \frac{2}{5}$.Solving for $x$:$14 - x = \frac{2}{5} 	imes 20 = 8$$x = 14 - 8 = 6$.Thus,$M_3$ produces $6$ defective bulbs out of $20$.The probability that a bulb chosen from $M_3$ is defective is $\frac{6}{20} = 0.3$.

Similar Questions

Bag $A$ contains $4$ green and $3$ red balls and bag $B$ contains $4$ red and $3$ green balls. One bag is selected at random and a ball is drawn,which is found to be green. What is the probability that it was drawn from bag $B$?

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:

Box $I$ contains $30$ cards numbered $1$ to $30$ and Box $II$ contains $20$ cards numbered $31$ to $50$. $A$ box is selected at random and a card is drawn from it. The number on the card is found to be a non-prime number. The probability that the card was drawn from Box $I$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module