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Winning Marble

Age 14 to 16 Short Challenge Level:

A prisoner is given a chance to win her freedom.

She is given two boxes and some marbles. She must put the marbles into the boxes.

Afterwards, she will be blindfolded, and will choose a box and select a marble. If she draws a white marble she will go free; otherwise, she will remain in prison.

The prisoner has 10 white marbles and 10 black marbles. She can put as many of the marbles of each colour as she likes into each box. She must use up all the marbles.

How can she maximise the probability that she will go free? In that case, what is the probability that she will go free?

This problem is taken from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.