Probability and Chance

Probability (sometimes known as ‘chance’) is a simple measurement of how likely something is, on a scale from 0 to 1. If there is no chance of something happening, its probability is zero. If something is absolutely certain, then its probability is considered to be one. Most events have a probability – or chance – somewhere between 0 and 1; you can, if you prefer, think of this in terms of percentages.

Simple probability with coins and dice

A simple example is the toss of a coin. One side is designated ‘heads’, the other ‘tails’. Assuming that the coin is equally weighted, and ignoring the slight possibility of it landing on an edge, then there is an equal chance of a ‘head’ or a ‘tail’ when the coin is tossed. We can say that there is a 50% chance of ‘heads’, or we can say that there’s a 50/50 chance (meaning 50% heads, or 50% not) or, to use correct probability terminology, we say that the probability is a half. This is written, of course, as 1/2 and can also be read as ‘one chance in two’.

A six-sided die, used in so many board games, has a one in six chance of landing on any particular number. Dice are likely to be of more interest to children as they play games, and it can be an interesting experiment to roll a die around a hundred times, marking down the number which results. In just a few rolls, it can be hard to spot any pattern: for instance you might roll two 5s, then a 2, then another 5, then a 3. But by the time you’ve rolled 60 times, you should see a roughly equal distribution – and the longer you continue the experiment, the more evenly, overall, you should see the pattern emerging.

Probability in life

Not everything is as straightforward as the toss of a coin or a die. Many professions rely on probabilities – for instance, weather forecasters predict the likelihood of rain; financial experts give estimates of the rise and fall of stocks and shares, or the relative value of different currencies. Insurance brokers calculate their premiums based on the probability of theft or illness for any particular house or individual. They look at patterns from the past, and current circumstances, and make predictions based on the information they have.

So, even though computers are used to calculate these things, it’s important to understand how probabilities work so that the right information can be entered, and also to check whether the results are reasonable. The word ‘probability’ means exactly that: you will probably see a pattern emerging. However, forecasters and insurance brokers sometimes make mistakes. A fit and healthy person might be struck with a debilitating illness. A freak hurricane might devastate several homes.

But, even with the roll of a die, the outcome is not definite. You might – just possibly – see a whole run of the same number, over and over again. You might see one number not appearing at all. Each time you roll, the probability of, say, a two is still one chance in six, even if you have rolled no twos at all. Equally, if you have just rolled three twos in a row, the probability of another two is still one in six. Patterns only emerge as you look at the bigger picture, over a larger number of trials.

If you don’t want the hassle of rolling a die and recording the result dozens of times, there’s a useful site that simulates the throw of large numbers of dice, showing the results each time as a bar chart with percentages at the bottom. See Throwing Dice Experiment.

Experimenting with probability

When children are interested in probabilities, but get bored with the throw of a die, it can be a good idea to make surveys based on their current interests. A young child on a car journey, for instance, could check off vehicles that pass, sorting them by colour, or type of vehicle, or even make of car, to see what the probabilities are and which are the most common. It’s highly unlikely that there will be an equal chance of red, yellow, blue or white cars, for instance. What does he think will be the most likely? What does he learn? Why does he suppose that a certain colour is a lot more popular than another?

More advanced probability

A bright child who has grasped the basic principles may ask what happens if toss two coins, or roll two dice. Indeed, many board games require the roll of a pair of dice, where the possible number total may be anything from 2 to 12, but the chances of different totals are not evenly matched. Perhaps this would be a useful experiment, to see what the distribution is over a large number of rolls.

There are many questions that may result. Why, for instance, is 7 more likely to be rolled than 2? What is the probability of a ‘double’ (ie the same number being rolled on two dice at the same time)?

The first can be answered by looking at the ways in which totals can be achieved. A 2 can only be rolled if both dice show 1. However, there are many ways in which 7 can be achieved. An introductory page like this cannot go into the depths of probability theory – see ‘further reading’ below if you are interested – but if a chart is made showing all the possible rolls of two die (36 in all, since each die can show any number from 1 to 6) it should become clear that 7 is the most likely combination, followed by 6 and 8, then 5 and 9, and so on.

Further reading:

Introduction to probability
Maths is fun: probability
Top marks: data handling (scroll down to find some games about simple probability)

 See also:

Writing fractions