Posts tagged: probability
Law of Large Numbers vs. the Gambler's Fallacy
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.
The Birthday Problem: Why 23 People Is Enough
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.
The Hot Hand
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 Monty Hall Problem: Why You Should Always Switch
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.
The Binomial Distribution: Counting Successes in Fixed Trials
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: Modeling Rare Events at a Known Rate
The Poisson distribution models counts of independent events occurring at a constant rate. One parameter does everything, and that turns out to be enough.
Discrete vs Continuous Distributions: PMF, PDF, and CDF
The difference between discrete and continuous probability distributions, explained through the PMF, PDF, and CDF, with cat examples that are doing actual work.