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}
