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# Winning Marble

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*

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Age 14 to 16

ShortChallenge Level

- Problem
- Solutions

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?

You can find more short problems, arranged by curriculum topic, in our short problems collection.

Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?

Which of these games would you play to give yourself the best possible chance of winning a prize?