# Probability Concepts

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Probability theory is a branch of mathematics that helps us understand random events. Probability is a measure of how likely an “event” is to occur.

In practical situations like finance, we often have to decide where some risk is involved. The logical and consistent tools we use to make such decisions are based on probability concepts.

Therefore, we need probability theory to handle many real-world problems that involve risks.

For example, we use probability tools to price bonds to consider the risk of default.

Probability is the likelihood of an “event occurring”.

Insurance companies use probability theory to help them decide what policies to offer and how much to charge. They use data about past events to calculate how likely a particular event will happen.

That data can help them decide, for example, whether or not to offer a policy for a particular type of car and how much to charge.

The probability of an event occurring can be expressed as a fraction between 0 and 1.

A fraction of 0 means that the event is impossible, while a fraction of 1 means that the event is sure to happen.

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## Table of content

∘ Random variable

∘ What is the outcome?

· What is an event?

∘ What is probability?

· Fraction method

· Looking for more educational content?

· What are the 2 defining properties of probability?

· Mutually Exclusive or disjoint

· Collectively exhaustive/jointly

· What is empirical probability?

· What is subjective probability?

· What is a priori probability?

· Stating probabilities as odds

· How do you calculate the odds of an event and the expected profit from a bet?

· Unconditional and Conditional probabilities

∘ Unconditional probability

· Conditional probability

· What is a joint probability?

· Multiplication rule

· Addition Rule

∘ Practice question: What is the probability of a limit order execution?

·…