What is Probability and Why Do We Use It?

Probability is a notion which we use to deal with uncertainty. If an event can have an number of outcomes, and we don't know for certain which outcome will occur, we can use probability to describe the likelihood of each of the possible events. The classic example is flipping a coin. There are two possible outcomes: the coin could come up heads or tails. Since we don't know which will occur, we say that there is a probability for each of the two events. Probabilities are denoted as numbers between $0$ and $1$, with $0$ meaning the outcome definitely will not occur and $1$ meaning it definitely will occur. You expect that if you flip a coin it is equally likely to come up heads or tails; the probability is $1/2$ for each outcome.

However, probability is not just any numeric expression of uncertainty between $0$ and $1$. It is defined in a particular way with specific rules of calculation. These rules will be discussed below. Probability calculus is not the only formalism for expressing uncertainty, but it is the most important. It is of fundamental importance in scientific reasoning, and is widely used to model uncertainty and random processes in scientific and engineering applications.