QJEEM24Ma3780: JEE Main 2024 Mathematics - Class 12 JEEM24Ma3780 Solution: Bag A contains 3 white, 7 red balls and Bag B contains 3 white, …

$\mathrm{E}_1: \mathrm{A}$ is selected

$\mathrm{E}_2: \mathrm{B}$ is selected

$\mathrm{E}$ : white ball is drawn

$\mathrm{P}\left(\mathrm{E}_1 / \mathrm{E}\right)=$

$\begin{aligned}& \frac{P(E) \cdot P\left(E / E_1\right)}{P\left(E_1\right) \cdot P\left(E / E_1\right)+P\left(E_2\right) \cdot P\left(E / E_2\right)}=\frac{\frac{1}{2} \times \frac{3}{10}}{\frac{1}{2} \times \frac{3}{10}+\frac{1}{2} \times \frac{3}{5}} \\& =\frac{3}{3+6}=\frac{1}{3}\end{aligned}$