Probability is a way of measuring how likely something is to happen. It's a number between 0 and 1, where 0 means the event is impossible and 1 means it's absolutely certain. An event with a probability of 0.5 has a 50/50 chance of occurring, like a coin flip landing on heads.

We calculate basic probability with a simple ratio. You count the number of ways a specific event can happen and divide that by the total number of possible outcomes.

For example, if you roll a single six-sided die, there is only one way to get a 4. Since there are six possible outcomes in total (1, 2, 3, 4, 5, 6), the probability of rolling a 4 is 1/6.

To calculate probability, we first need to understand all the possibilities. This complete set of all possible outcomes of an experiment is called the sample space.

An event, on the other hand, is a specific outcome or a collection of outcomes that we are interested in. It's a subset of the sample space.

In the diagram above, the sample space S includes all six possible outcomes of a die roll. The event A is the subset of outcomes where the roll is an even number. So, the probability of event A is the number of outcomes in A (which is 3) divided by the total number of outcomes in S (which is 6), giving us $P(A) = 3/6 = 1/2$.

Probabilities can be categorized based on the type of outcomes we are measuring. The two main types are discrete and continuous.

Think about the number of rainy days in a month, the result of a dice roll, or the number of students in a class. You can have 10 rainy days or 11, but you can't have 10.5. These are discrete values.

Examples include a person's exact height, the temperature of a room, or the time it takes to run a mile. Someone's height isn't just 175 cm or 176 cm; it could be 175.321 cm or any other value in between. The possibilities are infinite within the range.

While we can calculate the probability of a specific discrete outcome (like rolling a 3), it's impossible to calculate the probability of a single, exact continuous outcome. Why? Because there are infinitely many possibilities. The probability of someone being exactly 180.000... cm tall is effectively zero. Instead, with continuous data, we calculate the probability of an outcome falling within a certain range, like the probability of someone being between 179 cm and 181 cm tall.

These foundational ideas are the building blocks for understanding how we can use math to navigate the uncertainties of the world around us.