You have two bags, four red balls and four white balls. You must put all the balls in the bags although you are allowed to have one bag empty. How should you distribute the balls between the two. . . .

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

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?

Explore these X-dice with numbers other than 1 to 6 on their faces. Which one is best?

You and I play a game involving successive throws of a fair coin. Suppose I pick HH and you pick TH. The coin is thrown repeatedly until we see either two heads in a row (I win) or a tail followed by. . . .

Can you work out the probability of winning the Mathsland National Lottery? Try our simulator to test out your ideas.

If everyone in your class picked a number from 1 to 225, do you think any two people would pick the same number?

Imagine flipping a coin a number of times. Can you work out the probability you will get a head on at least one of the flips?

Invent a set of three dice where each one is better than one of the others?

Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea?

The next ten people coming into a store will be asked their birthday. If the prize is £20, would you bet £1 that two of these ten people will have the same birthday ?

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?

How do different drug-testing regimes affect the risks and payoffs for an athlete who chooses to take drugs?

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?

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.

By tossing a coin one of three princes is chosen to be the next King of Randomia. Does each prince have an equal chance of taking the throne?

In how many different ways can I colour the five edges of a pentagon red, blue and green so that no two adjacent edges are the same colour?