### 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?

# Put Out

##### Age 16 to 18Challenge Level

 There are 5 yellow balls in bag 1. One ball is transferred to bag 2 which contains an unknown number of green balls. Bag 2 is then shaken and a ball is selected at random and transferred to bag 1 without seeing its colour. Bag 1 is then shaken and a ball is selected at random and transferred to bag 2 without seeing its colour. Finally, a ball is chosen at random from bag 2.

If I tell you before you carry out this process that there's a $\frac{3}{5}$ chance you will end up with a green ball at the end, can you work out how many green balls are in bag 2 at the start?