Probability

Probability is a branch of mathematics that deals with the likelihood of a particular event or outcome occurring. It is used to quantify uncertainty and make informed decisions in various fields such as statistics, science, finance, and gaming.

Basic Concepts

There are several fundamental concepts in probability:

Sample Space: The set of all possible outcomes of an experiment. It is denoted by S.
Event: A subset of the sample space, representing a specific outcome or a combination of outcomes.
Probability of an Event: The likelihood of an event occurring, usually denoted by P(E), where E is the event.
Probability Scale: Probabilities range from 0 (impossible event) to 1 (certain event).

Calculating Probability

Probability can be calculated using different methods depending on the nature of the experiment:

Classical Probability: Involves equally likely outcomes, and the probability of an event E is calculated as P(E) = (Number of favorable outcomes) / (Total number of outcomes).
Empirical Probability: Based on observed data or experimental results. The probability of an event is estimated as the frequency of occurrence.
Conditional Probability: The probability of an event given that another event has occurred. It is denoted by P(E | F), where E and F are events.
Probability Rules: Include the addition rule, multiplication rule, and complement rule for calculating probabilities of compound events.