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

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. . . .

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?

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 ?

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. . . .

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

7 balls are shaken in a container. You win if the two blue balls touch. What is the probability of winning?

Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?

Your partner chooses two beads and places them side by side behind a screen. What is the minimum number of guesses you would need to be sure of guessing the two beads and their positions?

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?