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
| $E _1: A$ is selected | $A$ | $B$ |
|---|---|---|
| $3 W$ | $3 W$ | |
| $7 R$ | $2 R$ |
$E _2: B$ is selected
$E:$ white ball is drawn
$P\left(E _1 / E\right)=$
$\frac{P(E) \cdot P\left(E / E _1\right)}{P\left(E _1\right) \cdot P\left(E / E _1\right)+P\left(E _2\right) \cdot P\left(E / E _2\right)}=\frac{\frac{1}{2} \times \frac{3}{10}}{\frac{1}{2} \times \frac{3}{10}+\frac{1}{2} \times \frac{3}{5}}$
$=\frac{3}{3+6}=\frac{1}{3}$
