### Rain or Shine

Predict future weather using the probability that tomorrow is wet given today is wet and the probability that tomorrow is wet given that today is dry.

### Squash

If the score is 8-8 do I have more chance of winning if the winner is the first to reach 9 points or the first to reach 10 points?

### Snooker

A player has probability 0.4 of winning a single game. What is his probability of winning a 'best of 15 games' tournament?

# Dicey Dice

### Why do this problem?

Along with X-Dice, this is a great problem for thinking about conditional probability.

### Possible approach

Simply pose the challenge and encourage experimentation and calculation to begin with. There is no strictly 'linear' way into this problem: creativity and tinkering is required to end up with a valid set of dice. However, all students should eventually find a solution.

Once a set of dice with the correct properties has been invented and assessed move onto the question of the existence of a totally fair set of dice. You might begin this by asking who does or doesn't think that such a set of dice exists, using their intuitive reasoning. At the end, see who was correct.

### Key questions

How can we determine whether one die is likely to beat another?

### Possible extension

Investigate the variances of your set of dicey dice.

### Possible support

Simply invent pairs of dice and see which is better than the other.