### 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?

### 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.

### Nines and Tens

Explain why it is that when you throw two dice you are more likely to get a score of 9 than of 10. What about the case of 3 dice? Is a score of 9 more likely then a score of 10 with 3 dice?

# Misunderstanding Randomness

##### Stage: 3 Challenge Level:

Some definitions

random:
A term used in probability, relating to things that happen by chance. It means that there is no special pattern to the items or numbers that are selected or chosen, that is, they happen in a haphazard way.

random experiment:
Some process that is carried out according to a set of rules. The rules determine completely the process that we carry out, but they do not tell us in advance what the outcome of the experiment will be. A random experiment can be repeated arbitrarily often.

random number:
A sequence of randomly generated numbers, where all the numbers had an equal chance of being picked, every time. Tables of random numbers used to be printed in books, these days they're usually simulated on computers/calculators. They are used to select random samples in statistics.