At the beach, Ben and Katie introduce some basic ideas about probability. A scale in the sand is used to compare the likelihoods of some familiar events.

01.20—02.28

Lynne Suzanne tells Katie about some of the prizes she has scooped by entering competitions. Last year she entered about 500. We see how to calculate her probability of winning using the formula:

(probability) = (number of successful outcomes) ÷ (total number of possible outcomes)

02.28—03.36

Lynne takes Ben and Katie to a supermarket to look at the different types of competition. She prefers to enter competitions where you have to invent a slogan — she knows that fewer people enter these, so her chances of winning are increased. Lynne points out some different types of competition, and discusses the chances of being a winner.

03.36—04.10

Katie explains how one event can preclude another — and to illustrate the point they take a look in her kitchen cupboards.

04.10—06.18

Ben reveals the contents of another cupboard: seven tins without their labels. He uses a simple tree diagram to work out the probability of selecting a tin whose contents don’t go well with toast. Katie helps Ben by explaining the ‘or rule’. Not even Ben would eat the dog food they discover inside!

06.18—09.23

In ‘Tick or Trash’, Ben and Katie answer a question about picking a ball randomly from a bag containing several balls of different colours. Katie’s mistake is used to show how you can check the total probability, which should be 1, if you have correctly calculated the probabilities of all possible outcomes.

09.23—10.50

Ben visits Andrew Kingham, a marketing consultant, who explains how important probability is in designing competitions. He illustrates how both the likely popularity of a competition, and the cost to the company, are dependent on probability. Ben suggests putting £10 notes in bags of crisps, and Andrew discusses how probabilities would be used to determine how to set up such a marketing campaign. He demonstrates how to work out the probability of winning, and the cost of the campaign, for different numbers of £10 notes.

10.50—11.50

Ben has bought some crisps and chocolate, giving himself the chance to win a £10 note or a mobile phone. However, he hopes to win both the money and the phone. He calculates the combined probability by multiplying, and realises that his chances are very slim, so he decides to start scoffing the crisps instead.

11.50—end

Back in her kitchen Katie is still trying to get something to eat. She fancies a snack on toast. Unfortunately some of her bread is mouldy, and the tins have lost their labels. She uses a tree diagram to calculate the probability of choosing beans and an edible slice of bread. Having worked this out she makes her selection — and ends up with semolina and mouldy bread!