We don't live in a world of absolute certainties. Is it going to rain tomorrow? Will my favourite team win the match? Will I enjoy that new film? For most questions, the answer isn't a simple 'yes' or 'no'. It's usually a 'maybe'.

We naturally think in terms of likelihood. A weather forecast doesn't just say "rain" or "no rain". It gives a "30% chance of rain". This is a much more useful piece of information. It tells us the forecaster's degree of belief about rain, based on the data they have.

This is the core idea of probabilitys. It's a system for turning our feelings of uncertainty into numbers we can work with. Instead of just saying something is 'likely' or 'unlikely', we can be more precise.

To express our beliefs numerically, we use a simple scale that runs from 0 to 1.

• 0 means an event is impossible. The chance of a standard six-sided die landing on a 7 is 0.
• 1 means an event is certain. The chance that the sun will rise tomorrow is, for all practical purposes, 1.

Most events in life fall somewhere between these two extremes. A coin toss landing on heads has a probability of 0.5. It's perfectly in the middle, with an equal chance of happening or not happening.

This scale gives us a shared language for uncertainty. If someone says there's a 0.9 probability of their train being on time, you know they are very confident. If they say the probability is 0.2, you know they're not counting on it.

Before we look at any new evidence or data, we all have an initial idea of how likely something is. This starting point is our prior belief (or just 'prior' for short). It's our best guess based on what we already know about the world.

Imagine you're trying to guess if a new coffee shop in your town will be good. You haven't been there yet. What's your prior belief? If most coffee shops in your town are great, you might start with a high probability, say 0.8, that this one will also be good. If most are terrible, you might start with a much lower probability, like 0.3.

This initial belief isn't just a random guess. It’s based on your past experiences and general knowledge. It's the foundation upon which we build our reasoning. As we gather more information, like reading reviews or trying the coffee yourself, we can update this belief. But everyone has to start somewhere.

We often hear probabilities expressed as percentages, like that "30% chance of rain". To use these in calculations, we first need to convert them to the 0-to-1 scale we've been using.

The conversion is straightforward: just divide the percentage by 100. This is the same as moving the decimal point two places to the left.

Here are a few examples:

Thinking in decimals from 0 to 1 is the standard way to work with probability. It keeps the maths simple and consistent as we start to explore more complex ideas. Being able to quickly translate a percentage into a decimal is a fundamental first step.