Probability Explained

Summary:

Chapter 1 introduces the concept of probability and its importance in decision-making. Probability is based on mathematical theory and calculates the likelihood of events occurring. The chapter explains key terms such as experiment, sample space, and event.

An experiment is an act with unpredictable outcomes, and the sample space is the collection of all possible outcomes of the experiment. Events are subsets of the sample space that consist of specific outcomes.

The chapter provides examples to illustrate these concepts. For instance, when flipping a fair coin, the sample space is {heads, tails}, and the event of rolling a number larger than 3 on a dice is {4, 5, 6}.

It also introduces set theory and its application in probability. The union of two events represents the event where either one or both events occur, while the intersection represents the event where both occur. The complement of an event is the event that does not occur. Disjoint events are mutually exclusive, meaning they cannot occur simultaneously.

The chapter further discusses the probability measure and its axioms. The probability of an event is denoted as P(A), and it satisfies certain properties. For example, the probability of the sample space is always 1, and the probability of the empty set is 0. The probability of the union of two disjoint events is equal to the sum of their individual probabilities.

Methods for computing probabilities are explored, including counting techniques such as the multiplicative principle. Permutations and combinations are introduced, highlighting the difference between ordered and unordered samples.

Overall, Chapter 1 provides a foundation for understanding probability theory and lays the groundwork for further exploration of statistical inference.

Excerpt:

Probability Explained

CHAPTER 1

Probability

The idea around probability, chance and possibility is quite old and is commonly used in everyday speech. For example, what is the possibility that it will rain today, or what is the chance that your rugby team will win the match on Saturday? In everyday life, these chances and possibilities are based on people’s intuition-based guesses.

Probability is a concept founded on solid mathematical theory and can be a powerful aide in important decision-making.