Introduction to Probability — Part I

A brief introduction to probability basic concepts

What is Probability

When you do an experiment you get a certain set of outcomes. The certainty with which you can tell the possibility of getting a particular outcome is called Probability.

What is an Experiment

When you perform a certain procedure / task under controlled conditions which are always pre-planned then it is called an experiment.

Example :

1. Experiment : Rolling a fair dice for 500 times
2. Experiment : Tossing three fair coins for 10000 times.

What is Sample Space

When you perform an experiment you get some outcome. The set of all possible outcomes of an experiment is called Sample Space.

Example:

1. Experiment : Rolling a fair dice

Sample Space(S)={1,2,3,4,5,6}

1. Experiment : Tossing three fair coins

Sample Space(S) = {HHH,HHT,HTH,HTT,THH,THT,TTH,TTT}

What is an Event

An event is defined as certain collection of outcomes of an experiment. It is also called the subset of the Sample Space.

Example:

1. Experiment : Rolling a fair dice

Event A : Getting an even numbered outcome from S. A = {2,4,6}

Event B : Getting a number divisible by 3 from S. B = {3,6}

2. Experiment : Tossing three fair coins

Event A : Getting at-least 2 heads in the outcome.

A={HHH,HHT,HTH,THH}

Event B : Getting all tails.

B= {TTT}

What is AND vs OR Probability

Lets step back and think of the logical AND and OR operators:

1. Logical And : When the outcome satisfies both conditions at the same time.

2. Logical OR : When the outcome satisfies either or both of the conditions in question at a given time.

Let us understand the relevance in Probability through an example:

Example

1. Experiment : Draw a card from the deck of 52 cards.

A] AND

Sample Space S= {Spades, Diamonds, Hearts, Clubs}

Event A = {Diamonds, Spades}

Event B = {Black colored cards} = {Spades, Clubs}

A and B = {Spades }

B] OR

Event A = {Diamonds, Spades}

Event B = {Black colored cards}

A OR B = {Spades, Clubs, Diamonds}

References

Basic Statistics : https://www.shmoop.com/study-guides/math/basic-statistics-probability/and-or-probability