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’. Let’s assume that the coin is equally weighted, and ignore the slight possibility of it landing on an edge. There is, then, an equal chance of a ‘head’ or a ‘tail’ when we toss the coin. 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). Alternatively, we can say that the probability of ‘heads’ is a half. This is written as 1/2 and can also be read as ‘one chance in two’.

A six-sided die, used in 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 than coins, if they play games.  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. 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. Then they make predictions based on the information they have.

Even though computers are used to calculate these things, it’s important to understand how probabilities work. That means you can enter the right information. It also means that you can 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 always one chance in six. This is true even if you have rolled no twos at all so far. 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. It shows the results each time as a bar chart with percentages at the bottom. See Throwing Dice Experiment.

Experimenting with probability

Sometimes children are interested in probabilities, but get bored with the throw of a die. So it can be a good idea to make surveys based on their current interests. Young children on a car journey, for instance, could check off vehicles that pass. They could sort them by colour, or by type of vehicle, or even make of car. Then they can 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 do your children think will be the most likely? What do they learn? Why do they suppose that a certain colour is 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. When that happens, the possible number total may be anything from 2 to 12. But the chances of different totals vary. Perhaps it 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, are you more likely to roll 7 than 2? What is the probability of rolling a ‘double’ (ie the same number on two dice at the same time)?

You can answer the first question 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 you can roll a 7 . An introductory page like this cannot go into the depths of probability theory – see ‘further reading’ below if you are interested. But if you make a chart 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. It is 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:

Averages
Writing fractions