This article, for students and teachers, is mainly about probability, the mathematical way of looking at random chance and is a shorter version of Taking Chances Extended.

The King showed the Princess a map of the maze and the Princess was allowed to decide which room she would wait in. She was not allowed to send a copy to her lover who would have to guess which path. . . .

Can you design a bingo board that gives you the best chance of winning?

"Statins cut the risks of heart attacks and strokes by 40%"

Should the Professor take statins? Can you help him decide?

Newspapers said that eating a bacon sandwich every day raises the risk of bowel cancer by 20%. Should you be concerned?

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

A man went to Monte Carlo to try and make his fortune. Whilst he was there he had an opportunity to bet on the outcome of rolling dice. He was offered the same odds for each of the. . . .

Here are two games you have to pay to play. Which is the better bet?

Four cards are shuffled and placed into two piles of two. Starting with the first pile of cards - turn a card over... You win if all your cards end up in the trays before you run out of cards in. . . .

A gambler bets half the money in his pocket on the toss of a coin, winning an equal amount for a head and losing his money if the result is a tail. After 2n plays he has won exactly n times. Has. . . .

Two bags contain different numbers of red and blue marbles. A marble is removed from one of the bags. The marble is blue. What is the probability that it was removed from bag A?

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?

Use this animation to experiment with lotteries. Choose how many balls to match, how many are in the carousel, and how many draws to make at once.

This article, for students and teachers, is mainly about probability, the mathematical way of looking at random chance.

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?

Explore the distribution of molecular masses for various hydrocarbons

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. . . .

Investigate the molecular masses in this sequence of molecules and deduce which molecule has been analysed in the mass spectrometer.