Q. Bag $A$ contains $3$ white balls and $4$ black balls. Bag $B$ contains $3$ white and $2$ black balls. $A$ ball is transferred from $A$ to $B$ and then a ball is transferred from $B$ to $A$. The probability that $A$ again contains $3$ white and $4$ black balls, is
Probability
Solution:
The composition of bag $A$ remains the same if a white ball is transferred from $A$ to $B$ and then from $B$ to $A$ or a black ball is transferred from $A$ to $B$ and then from $B$ to $A$.
Bag A
Bag B
3W
3W
4B
2B
Required probability $= \frac{3}{7}\cdot\frac{4}{6}+\frac{4}{7}\cdot\frac{3}{6}$
$= \frac{24}{42} = \frac{4}{7}$
| Bag A | Bag B |
|---|---|
| 3W | 3W |
| 4B | 2B |