A bag contains 4 red and 3 black balls. A sec | vedclass

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

Question

(D) red ball can be drawn in two mutually exclusive ways.$(i)$ Selecting bag $I$ and then drawing a red ball from it.(ii) Selecting bag $II$ and then

Vedclass · Accepted Answer

$\frac{17}{35}$

Vedclass · Answer

(D) red ball can be drawn in two mutually exclusive ways.$(i)$ Selecting bag $I$ and then drawing a red ball from it.(ii) Selecting bag $II$ and then drawing a red ball from it.Let $E_1$,$E_2$ and $A$ denote the events defined as follows:$E_1 = 	ext{Selecting bag } I$$E_2 = 	ext{Selecting bag } II$Since one of the two bags is selected randomly,we have:$P(E_1) = \frac{1}{2}$ and $P(E_2) = \frac{1}{2}$Now,$P(A|E_1) = 	ext{Probability of drawing a red ball when the first bag is selected} = \frac{4}{7}$$P(A|E_2) = 	ext{Probability of drawing a red ball when the second bag is selected} = \frac{2}{5}$Using the law of total probability:$P(A) = P(E_1)P(A|E_1) + P(E_2)P(A|E_2)$$P(A) = \frac{1}{2} 	imes \frac{4}{7} + \frac{1}{2} 	imes \frac{2}{5}$$P(A) = \frac{2}{7} + \frac{1}{5} = \frac{10 + 7}{35} = \frac{17}{35}$

$A$ bag contains $4$ red and $3$ black balls. $A$ second bag contains $2$ red and $3$ black balls. One bag is selected at random. If from the selected bag,one ball is drawn at random,then the probability that the ball drawn is red,is

Similar Questions

Two cards are drawn at random and without replacement from a pack of $52$ playing cards. Find the probability that both the cards are black.

If $A_i$ $(i=1, 2, 3, \ldots, n)$ are $n$ independent events with $P(A_i) = \frac{1}{1+i}$ for each $i$,then the probability that none of $A_i$ occurs is

$A$ basket contains $5$ apples and $7$ oranges and another basket contains $4$ apples and $8$ oranges. If one fruit is picked out at random from each basket,then the probability of getting one apple and one orange is

Two marbles are drawn in succession from a box containing $10$ red,$30$ white,$20$ blue and $15$ orange marbles,with replacement being made after each drawing. Then the probability,that the first drawn marble is red and the second drawn marble is white,is

$A$ bag $X$ contains $2$ white and $3$ black balls,and another bag $Y$ contains $4$ white and $2$ black balls. If one bag is selected at random and one ball is drawn from it,what is the probability that the ball is white?

Vedclass Test Series

Exam Paper Generator

Online Exam Module