For any event that has multiple outcomes with different probabilities, it can be helpful and illustrative to construct a chart or diagram of the possible outcomes. Tree diagrams are a useful example ...

Every new piece of evidence reshapes what we thought we knew, and probability trees make that transformation visible. This is the quiet logic behind Bayesian reasoning, where certainty is never ...

Two events are independent if the probability of the first event happening has no impact on the probability of the second event happening. If the probability of one event happening affects the ...

The sum of the probabilities of all outcomes is 1. Independent events are those not affected by a previous event. The probability of two independent events both happening is 𝑃(A and B) = 𝑃(A) × 𝑃(B ...

The course is concerned with behavior of random walks on certain infinite graphs which are currently in vigorous development. This is a topic of dicrete probability are full of surprising and ...