### 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?

### Snooker

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

# Squash

##### Stage: 5 Challenge Level:

In the game of squash, players gain "points" by winning "rallies". If the "server" wins a rally, he or she wins a point; otherwise the service changes hands with no points gained.

Normally the game is won by the first player to reach 9 points -- typically by 2 or more points. But if the score reaches 8-8 then the person due to receive serve can call "9" (in which case the first to reach 9 wins) or call "10" (in which case the first to reach 10 wins).

I'm playing a game against Ivana Slogovitch, the Russian squash champion. I estimate that my chance of winning any particular rally against her, regardless of whether I serve or not, is p. The score gets to 8-8 and I am due to receive serve. Should I call "9" or "10"?