Probability for Machine learning and Data Science – Basic Probability Part 1 of 6

In this post, we will explore the basics of probability. As you have learned in school the set notations. we will explore all the symbols that are used to represent the sets. The contents of this post are

1. Sample Space
2. An Event
3. Set Notations

Sample Space

A sample space is defined as the set of all possible outcomes of a random experiment and it is denoted by \Omega.

Examples of sample spaces

1. The annual rate for rainfall in TamilNadu could take any non-negative value.
2. The number of cars passing at a given point on the national highway in one hour(This will take any non-negative integer).
3. The outcome of tossing 2 different coins.

Let us see the notation of each of the following

The annual rate for rainfall in TamilNadu could take any non-negative value.

\Omega = \{x|x \geq 0, x \in \R\}

The number of cars passing at a given point on the national highway in one hour(This will take any non negative integer).

\Omega = \{x|x = 0,1,2,3,...\}

The outcome of tossing 2 different coins

\Omega = \{HH, HT, TH, TT\}

Events

Events are denoted by A or B and it is a combination of outcomes and it is a subset of sample space \Omega

Examples of Events include

1. Rainfall less than 700mm in a year
2. Three cars passing a given point
3. Obtaining exactly 2 Heads

If we see these in notations

Rainfall less than 700mm in a year

A = \{x|0 \leq x \leq 700\}

Three cars passing a given point

B = \{3\}

Obtaining exactly 2 Heads

C = \{HH\}

Set Notations

Below are the commonly used set notations

Universial set : \Omega

Empty Set : \emptyset

Subset : A \subset B

Union : A \cup B

Intersection : A \cap B

Complement : A^c

Disjoint : A \cap B = \emptyset

We will see Probability Axioms in the next post

Happy Learning

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