Probability on emsenn.net

Conditional Probability and Independence

Thu, 01 Jan 2026 00:00:00 +0000

Audience: beginners learning how events relate.

Learning goal: explain conditional probability and independence.

Conditional probability updates the likelihood of an event when another event is known. Independence means knowing one event does not change the probability of another.

Check for understanding: How can you tell if two events are independent?

Counting and Events

Thu, 01 Jan 2026 00:00:00 +0000

Audience: beginners learning how to compute simple probabilities.

Learning goal: use counting to estimate probabilities of events.

When outcomes are equally likely, probability can be computed by counting favorable outcomes over total outcomes. Defining the sample space clearly keeps counting consistent. The tools for systematic counting — permutations, combinations, and binomial coefficients — are developed in combinatorics.

Check for understanding: Why does defining the sample space matter for counting?

Probability Overview

Thu, 01 Jan 2026 00:00:00 +0000

Audience: beginners learning about uncertainty.

Learning goal: define sample space, event, and probability in simple terms.

Probability assigns numbers to events in a sample space to represent how likely those events are. The total probability across all mutually exclusive outcomes adds to 1.

Check for understanding: What does it mean for probabilities to sum to 1?

Updating Beliefs with Bayes

Thu, 01 Jan 2026 00:00:00 +0000

Audience: beginners learning how evidence changes probability.

Learning goal: describe Bayes’ rule as updating prior beliefs with evidence.

Bayes’ rule combines a prior belief about an event with new evidence to produce an updated probability. It is useful when evidence is imperfect or uncertain.

Check for understanding: What role does new evidence play in Bayes’ rule?