IIT-JEE 1988Question 1
Urn $A$ contains $6$ red and $4$ black balls and urn $B$ contains $4$ red and $6$ black balls. One ball is drawn at random from urn $A$ and placed in urn $B$. Then one ball is drawn at random from urn $B$ and placed in urn $A$. If one ball is now drawn at random from urn $A$, the probability that it is found to be red is ______.
Probability
Answer$\dfrac{32}{55}$
Solution
Condition on the two transfers (red/red, red/black, black/red, black/black): $\frac6{10}\frac5{11}\frac6{10}+\frac6{10}\frac6{11}\frac5{10}+\frac4{10}\frac4{11}\frac7{10}+\frac4{10}\frac7{11}\frac6{10}=\frac{640}{1100}=\frac{32}{55}$.