# What researchers mean by... probability

If The Weather Network informs you that the probability of precipitation is 80 per cent for the day, it might prompt you to carry an umbrella.

We often use probability assessments informally in our daily lives to plan or make decisions. Formal probability theory is a fundamental tool used by researchers, health-care providers, insurance companies, stockbrokers and many others to make decisions in contexts of uncertainty.

Probability provides information about the likelihood that something will happen. Meteorologists, for instance, use weather patterns to predict the probability of rain. In epidemiology, probability theory is used to understand the relationship between exposures and the risk of health effects.

Let’s start with a simple, classic example to illustrate probability: the toss of a coin. You know intuitively that there is a 50 per cent chance of getting heads, and 50 per cent chance of getting tails. If you want to actually do the math to calculate the probability of a head, here’s the basic formula:

Count the number of times that the event will happen – in this case, there’s just one chance of a head appearing, so it’s 1. Divide this by the total number of possible outcomes. With a coin, it’s either heads or tails – which is 2 outcomes. So the probability of getting heads is 1÷2, or 50 per cent.

Yet you could toss a coin 10 times and get seven heads and three tails, which is 70 per cent heads and 30 per cent tails. With this small number of repetitions, you can’t determine the probability accurately. However, if you toss that coin 1,000 times or more – which a few people have done* – you will eventually begin to see that 50-50 breakdown.

This illustrates another important point about probability. It depends on the outcome or event happening over a large number of repetitions, or with a large number of people.

There are many examples of how probability is used throughout society. One common measure is the probability of developing cancer. According to the Canadian Cancer Society, 40 per cent of Canadian women and 45 per cent of men will have a diagnosis of an incident of cancer during their lifetimes. These probabilities are based on calculations from 2009 cancer statistics across the country.

While this broad information can be useful for those who plan, deliver or research health-care services, more detailed information is even more helpful. Researchers can also determine the probability of acquiring specific types of cancers at specific ages. They can also consider individual factors, which are important, too. If you have family members with breast cancer, your risk increases. If you smoke, your probability of getting lung cancer increases (smoking is estimated to account for between 88 and 90 per cent of lung cancer cases. The risk is significantly lower in never-smokers: about one per cent). These types of risk factors can be incorporated into probability calculations as well.

Another application of probability is with car insurance. Companies base your insurance premiums on your probability of having a car accident. To do this, they use information on the frequency of having a car accident by gender, age, type of car and number of kilometres driven each year to estimate an individual person’s probability (or risk) of a motor vehicle accident.

Probability can fall anywhere from 0 to 1, where 1 means there’s 100 per cent certainty that the event will occur. Zero means it will not.

So on a day in which the probability of precipitation was forecast at 80 per cent, but skies were sunny all day, you also have to consider that there was a 20 per cent chance that it wouldn’t rain. Still, you made a wise decision to take an umbrella based on the probability you were given.

*An English statistician tossed a coin 24,000 times around 1900. A total of 12,012 heads came up. During World War 2, an imprisoned South African mathematician tossed a coin 10,000 times and got 5,067 heads.
Ref: Moore, David S.; The Basic Practice of Statistics, 2nd ed.; WH Freeman and Company: New York, 2000.

Source: At Work, Issue 62, Fall 2010: Institute for Work & Health, Toronto