Tagged: probability

Probability rules, counting methods, and discrete distributions including binomial and Poisson.

The law of large numbers is a theorem. The gambler's fallacy is a mistake. They sound related and are easy to confuse. They say opposite things.

In a room of 23 people, the probability that two share a birthday exceeds 50%. The math is clean; the intuition resists it. Here's what's actually being counted.

Streaks in basketball shooting data and whether they reflect genuine elevated performance or expected clustering in random sequences. A case study in what random actually looks like.

The conditional probability problem that has produced more confident wrong answers than almost any other. The correct answer is 2/3, and the host's knowledge is why.

How the binomial distribution models the number of successes in a fixed number of independent trials, and why the formula looks the way it does.

The Poisson distribution models counts of independent events occurring at a constant rate. One parameter does everything, and that turns out to be enough.

The difference between discrete and continuous probability distributions, explained through the PMF, PDF, and CDF, with cat examples that are doing actual work.