Probability | Class 12 Mathematics Notes

Introduction

Probability is a branch of mathematics that deals with the study of random phenomena or experiments. It provides a quantitative description of the likelihood or chance of occurrence of an event. In everyday life, many situations involve uncertainty — for example, predicting the weather, the outcome of a cricket match, or the chance of getting a head when tossing a coin. Probability helps us to analyze such uncertain events mathematically. The study of probability began with the analysis of games of chance and has now become a fundamental tool in statistics, science, engineering, economics, and many other fields. The concept of probability allows us to assign a numerical value between 0 and 1 to an event, where 0 indicates impossibility and 1 indicates certainty. This chapter introduces the basic concepts of probability, including random experiments, sample spaces, events, and different approaches to defining probability. It also covers conditional probability, multiplication theorem, and independent events, providing a comprehensive foundation for understanding and calculating probabilities in various contexts.

📊 Diagram: No specific diagrams in this introductory section, but conceptual illustrations of random experiments like coin toss and dice roll are often used.

🧪 Activity: No specific activity in the introduction, but sets the stage for activities in later sections.

🔗 Connection: Leads to the next section on Random Experiment, Sample Space and Events, where these basic concepts are formally defined and illustrated.