**Probability **refers to the likelihood or chance of a specific event or outcome to occur. It is a measure that quantifies the uncertainty associated with various situations or events.

**Probability theory** is a concept which numerically measures the degree of uncertainty and certainty of the occurence of events.

• The concept of probability is essential for making informed decisions in the face of uncertainty.

**• Note**: Probability is typically expressed as a number between 0 and 1, where 0 indicates impossibility (the event will not occur), 1 indicates certainty (the event will occur), and values between 0 and 1 represent the likelihood of the event occurring.

## Points to be remembered:

**Deterministic**:

The phenomenon under which the result can be predicted with certainty is know as deterministic or predictable phenomenon.

**for example:**

- It is sure that night comes after the day and when a man is born, he must die sooner or later.

**Probabilistic:**

The phenomenon under which the result cannot be predicted with certainty is know as probabilistic or unpredictable phenomenon.

**for examples:**

- In toss of an fair coin, we are not sure of getting the head or tail.
- A producer cannot predict the future demand of his product with certainty.

## Basic Definitions of Various Terms Used in Probability Theory:

‣ **Experiment:**

A operation or action which produces result or outcome is called an **experiment**. **For example**, flipping a coin, rolling a die, or drawing a card from a deck are all experiments.

‣ **Random Experiment:**

A **random experiment **is an experiment for which the outcome is not predictable with certainty. It involves uncertainty, and the set of possible outcomes can be described by a sample space.

**For example**, flipping a fair coin is a random experiment because there are two possible outcomes (heads or tails) with equal probability of 1/2 each.

‣ **Trial and Event:**

Performing a random experiment is called a **trial**. The result of a random experiment is called an **event**.

**For example:-** Tossing of a coin is a trial or random experiment, and getting of a head or tail is an event.

‣ **Sample space:**

The set of all possible outcomes of a random experiment is called **sample space**.

• The possible outcomes are called **sample points**.

• The sample space is usually denoted by the letter ‘**S**‘ or ‘**Ω **‘.

**For example:**

In the case of flipping a fair, unbiased coin, the sample space (S) consists of all possible outcomes of the coin flip. Since a coin has two sides (heads and tails), the sample space is a set containing these two outcomes:

S={Heads, Tails}