What happened when a gambler asked for help from a mathematician? The formal study of Probability. Infinite Series is available to stream on pbs.org and the free PBS App, available on iPhone, Apple TV ...

A Markov chain is a sequence of random variables that satisfies P(X t+1 ∣X t ,X t−1 ,…,X 1 )=P(X t+1 ∣X t ). Simply put, it is a sequence in which X t+1 depends only on X t and appears before X t−1 ...

An animated guide to probability explains how to express probability as fractions and percentages based on the ratio of the number of ways an outcome can happen and the total number of outcomes.

Studies axioms, counting formulas, conditional probability, independence, random variables, continuous and discrete distribution, expectation, moment generating functions, law of large numbers, ...