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

Two coins are available, one fair and the other two-headed. Choose a coin and toss it once; assume that the unbiased coin is chosen with probability $\frac{3}{4}$. Given that the outcome is head, the probability that the two-headed coin was chosen, is

$A$ bag contains $2n+1$ coins. It is known that $n$ of these coins have heads on both sides,whereas the other $n+1$ coins are fair. One coin is selected at random and tossed. If the probability that the toss results in heads is $\frac{31}{42}$,then the value of $n$ is

In a certain city, the ratio of men to women is $5:4$. It is found that $80\%$ of men and $90\%$ of women are literate. If a person selected at random is found to be illiterate, then the probability that the person is a man is....

Bag $I$ contains $3$ red and $4$ black balls and Bag $II$ contains $4$ red and $5$ black balls. One ball is transferred from Bag $I$ to Bag $II$ and then a ball is drawn from Bag $II$. The ball so drawn is found to be red in colour. Find the probability that the transferred ball is black.

Vedclass Test Series

Exam Paper Generator

Online Exam Module