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## 'Fixing the Odds' printed from http://nrich.maths.org/

You have two bags, four red balls and four white balls. You must
put all the balls in the bags although you are allowed to have one
bag empty. Your friend chooses a bag at random and then chooses a
ball at random from that bag. How should you distribute the balls
between the two bags so as to make the probability that your friend
will choose a red ball as small as possible and what will the
probability be in that case?

How should you distribute the balls so as to make the
probability of choosing a red ball as large as possible and what
will the probability be in that case?

What happens if you have two bags, a hundred red balls and a
hundred white balls?