Theoretical probability

problem
Two's company

Age

11 to 14

Challenge level

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

Age

11 to 14

Challenge level

Are these games fair? How can you tell?
problem
Flippin' discs

Age

11 to 14

Challenge level

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

Age

5 to 7

Challenge level

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

Age

7 to 11

Challenge level

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?
problem
Fa cup

Age

16 to 18

Challenge level

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!
problem
Limiting probabilities

Age

16 to 18

Challenge level

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.
problem
Tricky track

Age

7 to 11

Challenge level

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?
problem
Put out

Age

16 to 18

Challenge level

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?
problem
Voting paradox

Age

14 to 18

Challenge level

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?