Question is that: From a total of $m$ white balls and $m$ black balls ($m>1$), $m$ balls are selected at random and put into a bag A, the remaining $m$ balls are put into bag B. A ball is then drawn randomly from each bag. Show that the probability that the two balls have the same colour is $\frac{m-1}{2m-1}$.
I have been working on this problem for one hour, but I have not clue.
Best Answer
The first ball is a certain color.
There are then $2m - 1$ remaining balls, each equally likely to be chosen as the second ball. Of those, $m-1$ are the same color as the first ball.
Hence: $P=\frac{m-1}{2m-1}$