Probability Question 8
Question 8 - 2024 (30 Jan Shift 2)
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 in white, is :
(1) $\frac{1}{4}$
(2) $\frac{1}{9}$
(3) $\frac{1}{3}$
(4) $\frac{3}{10}$
Show Answer
Answer (3)
Solution
| $\mathrm{E}_{1}: \mathrm{A}$ is selected | $\mathrm{A}$ | $\mathrm{B}$ |
|---|---|---|
| $3 \mathrm{~W}$ | $3 \mathrm{~W}$ | |
| $7 \mathrm{R}$ | $2 \mathrm{R}$ |
$\mathrm{E}_{2}: \mathrm{B}$ is selected
$\mathrm{E}:$ white ball is drawn
$\mathrm{P}\left(\mathrm{E}_{1} / \mathrm{E}\right)=$
$\frac{P(E) \cdot P\left(E / E_{1}\right)}{P\left(E_{1}\right) \cdot P\left(E / E_{1}\right)+P\left(E_{2}\right) \cdot P\left(E / E_{2}\right)}=\frac{\frac{1}{2} \times \frac{3}{10}}{\frac{1}{2} \times \frac{3}{10}+\frac{1}{2} \times \frac{3}{5}}$
$=\frac{3}{3+6}=\frac{1}{3}$
