### 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.

### Knock-out

Before a knockout tournament with 2^n players I pick two players. What is the probability that they have to play against each other at some point in the tournament?

### 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?

# FA Cup

##### Stage: 5 Challenge Level:

In the FA Cup 64 teams play a knockout tournament. Over the four years 2001, 2002, 2003 and 2004 Arsenal have been drawn against Chelsea each year and have beaten Chelsea every time. What is the probability of that happening?

Let's say that whenever Arsenal and Chelsea play the probability of Arsenal winning is 0.6 and otherwise, throughout the tournament, both these teams have a probability of winning of 0.7 in the first round, 0.6 in the second round and 0.5 in the subsequent rounds.