### 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

##### Stage: 5 Challenge Level:

You can use common sense for simple comparisons between dice, but where the relative probabilities are not obvious you can use the formula for conditional expectation:

$$P(A> B) = P(A> B|A=1)P(A=1)+\dots + P(A> B|A=6)P(A=6)$$