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The Lady or the Lions

The King showed the Princess a map of the maze and the Princess was allowed to decide which room she would wait in. She was not allowed to send a copy to her lover who would have to guess which path to follow. Which room should she wait in to give her lover the greatest chance of finding her?

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A Dicey Paradox

Four fair dice are marked differently on their six faces. Choose first ANY one of them. I can always choose another that will give me a better chance of winning. Investigate.

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Nine or Ten?

Is a score of 9 more likely than a score of 10 when you roll three dice?

Can't Find a Coin?

Age 11 to 14 Challenge Level:

Why do this problem?

In the context of trying to "fool the teacher", students may find that it is hard to make up the results of an experiment in a mathematically convincing way.

Possible approach

This might be a good start/end to a probability lesson, or a regular start/end to a series of lessons. Individual students could enter data 'live' on an interactive whiteboard, with the class anticipating whether the 'teacher' will be fooled.

Key questions

It could lead to good discussions
- why it is hard to imitate a 'memoryless' random experiment,
- developing a series of tests to check whether data are random.

Possible extension

Take a look at Introducing Distributions