Bag B₁ contains 6 white and 4 blue balls, Bag B₂ contains 4 white and 6 blue balls, and Bag B₃ contains 5 white and 5 blue balls. One of the bags is selected at random and a ball is drawn from it. If the ball is white, then the probability, that the ball is drawn from Bag B₂, is :

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

$\frac{2}{3}$

$\frac{2}{5}$

$\frac{1}{3}$

$\frac{4}{15}$

answer is B.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

E₁ : Bag B₁ is selected
B₁ B₂ B₃
6W 4B 4W 6B 5W 5B
E₂ : bag B₂ is selected
E₃: Bag B₃ is selected
A : Drawn ball is white
We have to find $P (\frac{E_{2}}{A})$

$\begin{array}{l} P (\frac{E_{2}}{A}) = \frac{P (E_{2}) P (\frac{A}{E_{2}})}{P (E_{1}) P (\frac{A}{E_{1}}) + P (E_{2}) P (\frac{A}{E_{2}}) + P (E_{3}) P (\frac{A}{E_{3}})} \\ = \frac{\frac{1}{3} \times \frac{4}{10}}{\frac{1}{3} \times \frac{6}{10} + \frac{1}{3} \times \frac{4}{10} + \frac{1}{3} \times \frac{5}{10}} \\ = \frac{4}{15} \end{array}$