Question

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

• A. $\frac{2}{7}$
• B. $\frac{3}{7}$
• C. $\frac{4}{7}$
• D. $\frac{2}{3}$

Answer 1

Answer: (C)

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 $=\frac{3}{7}\cdot \frac{4}{6}+\frac{4}{7}\cdot \frac{3}{6}$
$=\frac{24}{42}=\frac{4}{7}$