Theoretical probability

Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?

Are these games fair? How can you tell?

Discs are flipped in the air. You win if all the faces show the same colour. What is the probability of winning?

Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?

Have a go at this game which involves throwing two dice and adding their totals. Where should you place your counters to be more likely to win?

In four years 2001 to 2004 Arsenal have been drawn against Chelsea in the FA cup and have beaten Chelsea every time. What was the probability of this? Lots of fractions in the calculations!

Given probabilities of taking paths in a graph from each node, use matrix multiplication to find the probability of going from one vertex to another in 2 stages, or 3, or 4 or even 100.

In this game you throw two dice and find their total, then move the appropriate counter to the right. Which counter reaches the purple box first?

After transferring balls back and forth between two bags the probability of selecting a green ball from bag 2 is 3/5. How many green balls were in bag 2 at the outset?

Some relationships are transitive, such as `if A>B and B>C then it follows that A>C', but some are not. In a voting system, if A beats B and B beats C should we expect A to beat C?