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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.

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    $\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$
    – Community Bot
    Oct 2 at 4:28

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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: $P=\frac{m-1}{2m-1}$

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  • $\begingroup$ Thank you for your help, I think I understand now. $\endgroup$
    – user1228735
    Oct 2 at 11:34
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    $\begingroup$ Maybe, then, an accept ($\checkmark$) is in order? $\endgroup$
    – David G. Stork
    Oct 2 at 12:55

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