JEE MAIN - Mathematics (2024 - 30th January Evening Shift - No. 19)
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
1/4
1/3
3/10
1/9
Explanation
_30th_January_Evening_Shift_en_19_1.png)
$$\mathrm{E}_1: \mathrm{A}$$ is selected
$$\mathrm{E}_2: \mathrm{B}$$ is selected
$$\mathrm{E}$$ : white ball is drawn
$$\mathrm{P}\left(\mathrm{E}_1 / \mathrm{E}\right)=$$
$$\begin{aligned} & \frac{P(E) \cdot P\left(E / E_1\right)}{P\left(E_1\right) \cdot P\left(E / E_1\right)+P\left(E_2\right) \cdot P\left(E / E_2\right)}=\frac{\frac{1}{2} \times \frac{3}{10}}{\frac{1}{2} \times \frac{3}{10}+\frac{1}{2} \times \frac{3}{5}} \\ & =\frac{3}{3+6}=\frac{1}{3} \end{aligned}$$
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