Introduction

This section introduces the basics of probability, including its importance in quantifying uncertainty and predicting outcomes.

Key Concepts & Vocabulary

This section introduces foundational probability concepts such as experiments, outcomes, events, and probability itself.

Experiment / Trial

An experiment or trial involves a process with uncertain outcomes, which forms the basis for understanding probability.

Outcome

This section discusses outcomes in probability, explaining their significance and relation to events and sample spaces.

Sample Space (S)

The sample space represents the complete set of all possible outcomes for a given experiment, forming the foundation of probability theory.

Event

This section introduces the concept of events in probability, explaining their relationship to the sample space and how they can be analyzed in terms of likelihood.

Probability (P)

This section introduces the fundamental concepts of probability, its types, rules, and applications, highlighting its importance in quantifying uncertainty.

Defining Probability

This section provides a comprehensive overview of probability, covering theoretical, empirical, and subjective approaches, along with essential properties and key concepts.

Classical (Theoretical) Probability

Classical probability deals with the likelihoods of events occurring in situations with equally likely outcomes.

Empirical (Experimental) Probability

Empirical probability is determined through observation and experimentation rather than theoretical calculations.

Subjective Probability

Subjective probability is based on personal judgment and experience rather than strict calculation.

Properties Of Probability

This section focuses on the key properties of probability, including fundamental rules and concepts that quantify the likelihood of events in various scenarios.

Venn Diagrams

Venn diagrams are visual tools that illustrate relationships between different events, showing their intersections, unions, and complements within a probability context.

Worked Example

This section presents a worked example demonstrating how to calculate probabilities using a simple die roll.

Conditional Probability

This section focuses on conditional probability, exploring how the probability of an event is influenced by the occurrence of another event.

Independent Events

Independent events are those whose occurrence does not affect each other's probabilities.

Mutually Exclusive Vs Independent

This section explores the differences between mutually exclusive events and independent events in probability theory.

Bayes’ Theorem (Introductory)

Bayes’ Theorem provides a way to update the probability of an event based on new evidence, allowing for more informed decision-making.

Probability Distributions (Discrete)

This section covers discrete probability distributions, explaining how probabilities are assigned to specific outcomes and introducing key concepts such as expected value and variance.

Binomial Probability (Basic Intro)

This section introduces the concept of binomial probability, focusing on calculating the likelihood of achieving a specific number of successes in independent trials.

Common Pitfalls

This section highlights common misconceptions and mistakes related to probability.

Exercises (Examples)

This section presents exercises related to probability concepts, including card drawing, coin tossing, and traffic light scenarios.

Exercise 1

This section introduces basic probability concepts through various exercises related to classical and empirical probability.

Exercise 2

Exercise 2 focuses on practical applications of probability concepts through engaging problems.

Exercise 3

This section presents exercises that apply the concepts of probability learned in the chapter, reinforcing the understanding through practical scenarios.

Summary

This section covers the essential concepts of probability, highlighting how to measure uncertainty and predict outcomes of random events.