Theoretical probability

Are these games fair? How can you tell?

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

Engage in a little mathematical detective work to see if you can spot the fakes.

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?

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

Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?

Is a score of 9 more likely than a score of 10 when you roll three dice?

Which of these games would you play to give yourself the best possible chance of winning a prize?

Here are two games you can play. Which offers the better chance of winning?