Real-world probability

Probability is perhaps one of the topics from school mathematics that are used most often in the real world. We use ideas of probability all the time, often without really thinking about them. When was the last time you:

• planned a journey?
• read a weather forecast?
• bought a new item from a website?

All of these situations involve a degree of risk or uncertainty; that new pair of shoes that you want to order may look great on the website, but how sure can you be that ‘your size’ will actually fit? And how much attention should you give to the customer reviews?

Probability provides the mathematical tools to deal with uncertainty, in a wide range of situations. Here, for example, is a description of the approach to probability in weather forecasting taken by the UK Met Office:

Predicting how the weather will behave over the coming hours, days, weeks and months is a complex undertaking. Each timescale presents its own challenges. In an ideal world, everyone would like us to tell them exactly what the weather will do so they can make definite decisions in their local area.

Nature, however, doesn’t work like that. But one thing we can do is tell people about the probabilities of things happening.

In the short range, it is possible to predict with a high degree of accuracy what the weather has in store. However, the science does not exist to allow precise prediction of local details five days ahead. When severe weather may be on the way, it may be very unpredictable even in the short term. In these situations, uncertainty, or risk, becomes increasingly important in weather forecasting.

To forecast the weather we first gather observations from around the world to measure what the atmosphere is doing. We use these observations to set up a computer simulation of the atmosphere that represents what is happening right now. The model then calculates how the atmosphere will evolve over the coming days. Unfortunately, due to chaos, small unknowns in our observed atmosphere can grow rapidly to give large uncertainties in the forecast.

Over the last 15 years, the Met Office has developed sophisticated techniques to understand these uncertainties, called ensemble forecasts. This means we run our simulations many times instead of just once, from very slightly different starting conditions. The range of different outcomes gives us a measure of how confident or uncertain we should be in the overall forecast. On some occasions the uncertainty is quite small and we can be confident – other times much less so. This can help decision makers manage the risks associated with the weather.

Using ensembles is good science and it lets us give an indication of our certainty in a forecast. But it also presents us with a problem. How do we effectively communicate the forecast, both the bits we can be confident about and the areas where we are less confident? How can we communicate probabilities?

The Met Office is already beginning to provide more probability based information on its website. This includes information on the chance of rain and the possible range of maximum and minimum temperatures for our 5000 or so location forecasts available online. Furthermore we are using probability information within our National Severe Weather warnings and are at times supporting these with additional images and videos to explain possible severe weather.

What other practical applications of probability can you think of?