Chapter_4_Slides_Jaggia1

Fundamental Probability Concepts

Basic principles guiding the analysis of uncertainty and likelihood of events.

Statistical Experiment

A process that leads to one of several possible outcomes, sometimes referred to as a random experiment.

Sample Space (S)

The set of all experimental outcomes generated by an experiment.

Probability

A numerical measure of the likelihood of occurrence of an event.

Exhaustive Events

Events that include all possible outcomes of an experiment.

Mutually Exclusive Events

Events that cannot occur at the same time; the occurrence of one event precludes the occurrence of another.

Complement of an Event (Ac)

The event consisting of all sample points not in event A, such that P(A) + P(Ac) = 1.

Addition Law of Probability

A formula to compute the probability of the occurrence of at least one of two events: P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

Conditional Probability

The probability of an event given that another event has occurred, denoted by P(A|B).

Independent Events

Events whose probabilities do not affect each other; P(A|B) = P(A).

Multiplication Law

A formula used to compute the probability of the intersection of two events: P(A ∩ B) = P(A) * P(B|A).

Contingency Table

A table used to summarize the relationship between two categorical variables, showing frequencies for each combination of categories.

Empirical Probability

Probability derived from observed data and frequencies of events occurring in an experiment.

Classical Probability

Probability based on the assumption of equally likely outcomes.

Total Probability Rule

Used to compute the total probability of an event based on different conditions or partitions of the sample space.

Bayes’ Theorem

A method to calculate conditional probabilities and update the probability estimate for an event based on new evidence.