Probability is simply a way to measure how likely something is to happen. We use it all the time, even if we don't think about it. When a weather app says there's a 70% chance of rain, it's talking about probability. It's a number between 0 and 1 that quantifies uncertainty.

For example, the probability of a standard six-sided die landing on a 7 is 0. It can't happen. The probability that it will land on a number less than 7 is 1, because that covers all the possible outcomes.

Most events fall somewhere in between. A coin flip has a 0.5 probability of landing on heads. This doesn't mean you'll get heads exactly half the time in a few flips, but it's the long-term expectation. The basic formula to calculate the probability of an event is:

Let's stick with the die roll. What's the probability of rolling a 4? There's only one way to get a 4 (a favorable outcome) and six possible outcomes in total (1, 2, 3, 4, 5, 6). So, the probability is $1/6$.

To calculate probability, we first need to know all the things that could happen. In probability, this complete set of all possible outcomes is called the sample space.

An event is a specific outcome or a set of outcomes you're interested in. It's a subset of the sample space. For example, rolling an even number on a die is an event. The outcomes that satisfy this event are {2, 4, 6}, which is a part of the die's full sample space.

Here, the probability of event A (rolling an even number) is the number of outcomes in A divided by the total number of outcomes in S. That's 3 favorable outcomes divided by 6 total outcomes, so $P(A) = 3/6 = 1/2$.

Probability isn't arbitrary; it follows a few straightforward rules. These are often called the axioms of probability, and they provide the foundation for everything else.

For instance, you can't roll a 1 and a 3 on a single die at the same time. These events are mutually exclusive. The probability of rolling a 1 is $1/6$, and the probability of rolling a 3 is also $1/6$. So, the probability of rolling a 1 or a 3 is:

These three principles are the building blocks we use to navigate the world of chance. They allow us to make sense of uncertainty in a logical, consistent way.

Understanding these core ideas is the first step toward using probability to make better decisions, whether you're playing a board game or evaluating a business risk.