Bag A contains 3 white, 7 red balls and Bag B contains 3 white, 2 red balls.

Question

Bag A contains 3 white, 7 red balls and Bag B contains 3 white, 2 red balls. One bag is selected at random and a ball is drawn from it. The probability of drawing the ball from the bag A, if the ball drawn is white, is

Accepted Answer

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

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

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

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

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

Solutions · 1