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Quantitative Finance by Matt Davison

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Appendix 1: Probability Theory Basics

A1.1 Introduction

When facing uncertainty, decision making could be hard. Sometimes, simply examining the outcomes is already very useful in making a decision. We have a special mathematical word for outcomes; we call them “events.”

We suppose the events (possible individual outcomes) A, B, C, and so on are subsets of sample space S (possible all outcomes).

Event A or B happens—in set theory language, AB (reads A union B).

Event A and Event B both happen—in set theory language, AB (reads A intersection B).

Event A does not happen—in set theory language. Ac (reads A complement).

(Exclusive or—either A or B happen but not both—ABAB).

Venn diagrams are a good way to visualize these.

The concepts of

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