A bag X contains 2 white and 3 black balls an | vedclass

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

Question

(C) Let $E_1$ be the event of selecting bag $X$ and $E_2$ be the event of selecting bag $Y$. Since the bag is selected at random, $P(E_1) = P(E_2) = \

Vedclass · Accepted Answer

$\frac{8}{15}$

Vedclass · Answer

(C) Let $E_1$ be the event of selecting bag $X$ and $E_2$ be the event of selecting bag $Y$. Since the bag is selected at random, $P(E_1) = P(E_2) = \frac{1}{2}$.Let $W$ be the event of drawing a white ball.The probability of drawing a white ball from bag $X$ is $P(W|E_1) = \frac{2}{2+3} = \frac{2}{5}$.The probability of drawing a white ball from bag $Y$ is $P(W|E_2) = \frac{4}{4+2} = \frac{4}{6} = \frac{2}{3}$.Using the law of total probability, the probability of drawing a white ball is $P(W) = P(E_1) \cdot P(W|E_1) + P(E_2) \cdot P(W|E_2)$.$P(W) = \left(\frac{1}{2} \cdot \frac{2}{5}\right) + \left(\frac{1}{2} \cdot \frac{2}{3}\right) = \frac{1}{5} + \frac{1}{3} = \frac{3+5}{15} = \frac{8}{15}$.

$A$ bag $X$ contains $2$ white and $3$ black balls and another bag $Y$ contains $4$ white and $2$ black balls. One bag is selected at random and a ball is drawn from it. Then, the probability for the ball chosen to be white is:

Similar Questions

If $x$ is real,then the value of $\frac{x^2-3x+4}{x^2+3x+4}$ lies in the interval

On heating a mixture of $SO_2Cl_2$ and $CO$,two equilibria are simultaneously established:
$SO_2Cl_{2(g)} \rightleftharpoons SO_{2(g)} + Cl_{2(g)}$
$CO_{(g)} + Cl_{2(g)} \rightleftharpoons COCl_{2(g)}$
On adding more $SO_2$ at equilibrium,what will happen?

If $\overline{a}, \overline{b}, \overline{c}$ are non-coplanar unit vectors such that $\overline{a} \times (\overline{b} \times \overline{c}) = \frac{\overline{b} + \overline{c}}{\sqrt{2}}$,then the angle between $\overline{a}$ and $\overline{b}$ is

Which of the following concepts best explains why $o-$nitrophenol is more volatile than $p-$nitrophenol?

Consumption of which one of the following foods can prevent the kind of blindness associated with vitamin-$A$ deficiency?

Vedclass Test Series

Exam Paper Generator

Online Exam Module