Balls & Urns

[Tiberius]

An easy one for you today

You have 101 coloured balls. There are 51 red balls and 50 blue balls.

You have two urns and have to put all of the balls into these. You can split them up any way that you want.

Now your friend has to pick one urn at random, put his hand in and choose one of the balls it contains (without looking!)

How should you have split the balls between the urns to maximize the chance that he will pick a red ball?

Answer:

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Put one red ball in one urn. Put the other 50 red balls and the 50 blue balls in the other urn.

That way, one urn has a 100% chance of returning a red ball, and the other has a 50% chance. So the chances of your friend getting a red ball are:

0.5 * 1 + 0.5 * 0.5 = 0.75 (or 75%)

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