Question

A bag $x$ contains $3$ white balls and $2$ black balls and another bag $y$ contains $2$ white balls and $4$ black balls. A bag and a ball out of it are picked at random. The probability that the ball is white is

• A. $\frac{3}{5}$
• B. $\frac{7}{15}$
• C. $\frac{1}{2}$
• D. None of these

Answer 1

The correct option is B

$\frac{7}{15}$

Explanation for the correct option:

Find the probability of getting white ball:

Let $E_1$ be the event of picking the bag $x$ and $E_2$ be the event of picking the bag $y$

Also, let W be the event of getting white ball.

Then, $P\left(E_1\right)=P\left(E_2\right)$

$=\frac{1}{2}$

The probability of drawing the white ball from bag $x$ is $P\left(\frac{W}{E_1}\right)=\frac{3}{5}$

The probability of drawing the white ball from bag $y$ is $P\left(\frac{W}{E_2}\right)=\frac{2}{6}$

$\therefore$The required probability is $P\left(W\right)=P\left(E_1\right).P\left(\frac{W}{E_1}\right)+P\left(E_2\right).P\left(\frac{W}{E_2}\right)$

$=\frac{1}{2}\times \frac{3}{5}+\frac{1}{2}\times \frac{2}{6}$

$=\frac{3}{10}+\frac{1}{6}$

$=\frac{(9+5)}{30}$

$=\frac{14}{30}$

$=\frac{7}{15}$

Hence, option ‘B’ is correct.