Provide Information Regarding Statistics & Econometrics : Introduction to Probability Lecture 17

Introduction to Probability

Lecture 17

Probability is a quantitative measure of the likelihood of an event occurring.

Probability is a subject that may be divided into two main areas.

Subjective Probability

Subjective probability is a sort of probability that is based on a person's own experience, intuition or some other indirect information regarding the likelihood of a particular result. It just represents the subject's beliefs and prior experiences; it doesn't include any required calculations.

Objective Probability

The likelihood that an event will occur based on the analysis of concrete measurements rather than intuition or conjecture is known as objective probability. Every measure is a hard fact, an observation that has been documented, or a piece of a large set of data. The probability estimate is calculated by manipulating the data with mathematical equations to determine the probability of an independent event occurring.

Terms Used in Probability and Statistics

There are various terms utilized in the probability and statistics concepts, such as:

Random Experiment

An experiment whose outcome is unknown and cannot be predicted.

For example, we cannot predict the outcomes when a coin is toss at random. Any output between head and tail is possible. This experiment is therefore random.

Sample Space

A set of all possible outcomes of a random experiment. The sample space is denoted by S.

e.g.;

i. The sample space when a coin is tossed once.

S = {H, T}

ii. The sample space when a die is rolled once.

S = {1, 2, 3, 4, 5, 6}

Event

Any subset of a sample space. The event is denoted by the capital letters of the English alphabet.

Let S = {1, 2, 3, 4, 5, 6}

Let A represent the even number.

A = {2, 4, 6}

It can be stated as:

Mutually Exclusive Events

In a random experiment, two events are considered mutually exclusive if they cannot occur simultaneously in the same trial.

Let A and B are two mutually exclusive events, then mathematically it can be expressed as:

Exhaustive Events

Two or more events are said to be mutually exclusive events when the union of mutually exclusive events gives the entire sample space.

Mathematically, it can be written as:

Equally Likely Events

Two events A and B are said to be equally likely when the occurrence is as likely to occur as the other.

Combination

Any order arrangement of r objects from n objects.

e.g., in how many ways are 2 persons selected from 5 persons without considering order?

Permutation

An order arrangement of r objects from n objects.

e.g., in how many ways are 2 people selected so that the first is president and the second is secretary from 10 persons?

Tree Diagram

A tree diagram is an instrument constructed up of line segments that extend from both the starting point and the outcome point. It is used to determine all possible outcomes of a probability experiment, as well as list those possible outcomes in an organized manner.

Example 5.1: Draw a tree diagram when a coin is two times.