Contextualization

Probability is a branch of mathematics that studies the chances of a particular outcome occurring in a random experiment. This field of study has applications in many areas of everyday life, such as meteorology, insurance, medicine, social sciences, and even sports. To understand the basic theory of probability, we first need to know the concepts of sample space, event, and random event.

The sample space, denoted as S, is the set of all possible outcomes of a random experiment. For example, when we flip a coin, the sample space is S = {heads, tails}. An event is a subset of a sample space. A random event is an event whose outcome is determined by chance and not by a predetermined set of conditions.

The calculation of the probability of an event is usually expressed as a number between 0 and 1, or equivalently, between 0% and 100%. A probability of 0 means that the event is impossible, while a probability of 1 indicates that the event is certain. Probability theory tells us how to calculate these probabilities and how to combine them to calculate the probabilities of more complex events.

Probability has vast applications in various areas. In medicine, for example, it is used to estimate the likelihood of a patient having a particular disease based on their symptoms or test results. In data science, probability is used to make predictions about future data based on past data. In economics, probability can be used to model uncertainties about future prices of financial assets and help in decision-making.

As a reliable resource for further study on the topic, we recommend the book [