Puzzle #8: Maximizing the Odds

Here is a cute problem given to me by a friend, who mentioned that this was part of the Martin Gardner collection.

There are two identical urns, and there are 50 identical red balls and 50 identical white balls. All the balls are distributed between the two urns. You will perform a two step process as follows:

1. Choose one of the urns at random

2. Choose a ball within the chosen urn at random

Your task is to maximize the probability of getting a red ball. How would you distribute the balls between the two urns?

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