One bag contains 5 white and 3 black balls an | vedclass

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

Question

(B) Let $W_1$ be the event of drawing a white ball from the first bag and $B_1$ be the event of drawing a black ball from the first bag.Total balls in

Vedclass · Accepted Answer

$\frac{5}{8}$

Vedclass · Answer

(B) Let $W_1$ be the event of drawing a white ball from the first bag and $B_1$ be the event of drawing a black ball from the first bag.Total balls in the first bag $= 5 + 3 = 8$.$P(W_1) = \frac{5}{8}$ and $P(B_1) = \frac{3}{8}$.After transferring one ball,the second bag contains $2 + 4 + 1 = 7$ balls.Case $1$: If a white ball is transferred,the second bag now contains $2 + 1 = 3$ white and $4$ black balls.Probability of drawing a black ball from the second bag given $W_1$ is $P(B_2|W_1) = \frac{4}{7}$.Case $2$: If a black ball is transferred,the second bag now contains $2$ white and $4 + 1 = 5$ black balls.Probability of drawing a black ball from the second bag given $B_1$ is $P(B_2|B_1) = \frac{5}{7}$.Using the Law of Total Probability:$P(B_2) = P(W_1) 	imes P(B_2|W_1) + P(B_1) 	imes P(B_2|B_1)$$P(B_2) = (\frac{5}{8} 	imes \frac{4}{7}) + (\frac{3}{8} 	imes \frac{5}{7})$$P(B_2) = \frac{20}{56} + \frac{15}{56} = \frac{35}{56} = \frac{5}{8}$.

One bag contains $5$ white and $3$ black balls and a second bag contains $2$ white and $4$ black balls. One ball is drawn from the first bag and placed unseen in the second bag. What is the probability that a ball now drawn from the second bag is black?

Similar Questions

$A$ committee consists of $9$ experts taken from three institutions $A, B$ and $C$,of which $2$ are from $A, 3$ from $B$ and $4$ from $C$. If three experts resign,then the probability that they belong to different institutions is

Three coins are tossed together,then the probability of getting at least one head is

Study the given information carefully to answer the question that follows. An urn contains $4$ green,$5$ blue,$2$ red and $3$ yellow marbles. If $3$ marbles are drawn at random,what is the probability that none is green?

If $A$ and $B$ are two events such that $P(A) = \frac{3}{8}$,$P(B) = \frac{5}{8}$ and $P(A \cup B) = \frac{3}{4}$,then $P(A|B) = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module