Theoretical probability

Kaia is sure that her father has worn a particular tie twice a week in at least five of the last ten weeks, but her father disagrees. Who do you think is right?

It is believed that weaker snooker players have a better chance of winning matches over eleven frames (i.e. first to win 6 frames) than they do over fifteen frames. Is this true?

Two brothers belong to a club with 10 members. Four are selected for a match. Find the probability that both brothers are selected.

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?

This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.

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.

Are these statistical statements sometimes, always or never true? Or it is impossible to say?

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!

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?

Imagine a room full of people who keep flipping coins until they get a tail. Will anyone get six heads in a row?