Probability — the basics

A probability is a number between 0 and 1 that expresses how strongly we believe something will happen.

Event

A possible outcome ("it rains tomorrow").

Probability P(A)

How likely event A is. P(rain) = 0.3 = 30 %.

Independent events

One doesn’t affect the other. Coin flips.

Distribution

A map from every event to its probability.

Binomial question

When the same yes/no event repeats, a binomial model estimates how often one outcome appears.

normal distribution

Many measured quantities cluster around a middle value, with rarer values farther away.

Monte Carlo simulation

When a formula is awkward, run many random trials in code and inspect the distribution of outcomes.

A simple distribution

Heights show the probability of each outcome.

Applied frame

Translate the claim into events, probabilities, distributions, and simulation checks before trusting a single answer.

Diagram cue

The diagram separates event space, probability mass, evidence, and update steps.