Probability fundamentals are the cornerstone of understanding and analyzing uncertainty. In this section, we'll explore the basic concepts and principles that form the basis of probability theory.
Key Concepts
Probability Space: A probability space is a mathematical construct that allows us to model random experiments. It consists of three elements: a sample space, events, and a probability measure.
Sample Space: The sample space is the set of all possible outcomes of a random experiment.
Event: An event is a subset of the sample space. It represents a particular outcome or a combination of outcomes.
Probability Measure: The probability measure assigns a probability between 0 and 1 to each event, representing the likelihood of its occurrence.
Types of Probability
Objective Probability: Objective probability is based on physical or empirical evidence. It is often used when the probability of an event can be measured or estimated.
Subjective Probability: Subjective probability is based on an individual's belief or judgment. It is often used when there is no empirical evidence available.
Basic Probability Rules
Addition Rule: The probability of the union of two events is equal to the sum of their individual probabilities minus the probability of their intersection.
Multiplication Rule: The probability of the intersection of two independent events is equal to the product of their individual probabilities.
Complement Rule: The probability of an event is equal to 1 minus the probability of its complement.
Resources
For more in-depth understanding of probability fundamentals, you can explore the following resources: