How can 20 balls, 10 white and 10 black, be put into two urns so as to maximize the probability of drawing a white ball if an urn is selected at random and a ball is drawn at random from it?

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- Feb 4th 2010, 09:12 AMnovas51791Two Urns Problem
How can 20 balls, 10 white and 10 black, be put into two urns so as to maximize the probability of drawing a white ball if an urn is selected at random and a ball is drawn at random from it?

- Feb 4th 2010, 10:12 AMSoroban
Hello, novas51791!

This is a classic (very old) puzzle.

Quote:

How can 20 balls, 10 white and 10 black, be put into two urns

so as to maximize the probability of drawing a white ball

if an urn is selected at random and a ball is drawn at random from it?

Solution: .

We have: .

. .

. . Hence: .

. .

. . Hence: .

Therefore: .

- Feb 4th 2010, 10:32 AMnovas51791
Thank you so much! That's the answer I got as well, from guessing and checking.

Is it just a matter of guessing and checking, or is there some mathematical way to obtain that answer? Thanks!