🎰 What if the rat has more than two doors? Two names to know: categorical (one pick among many) and multinomial (counts across many picks).

Bernoulli and binomial only allow two outcomes. Put the rat in an n-armed maze and each arm i gets its own probability pᵢ. A single choice among them is a draw from a categorical distribution — just a weighted die. As always, the probabilities have to account for everything, so they sum to 1:

Σᵢ pᵢ = 1

All the arm-probabilities add up to 1 — the rat definitely picks *some* arm.

Repeat that pick many times and tally how often each arm was chosen — that tally follows the multinomial distribution. The clean way to remember the whole family:

• Bernoulli → one flip, 2 outcomes
• Binomial → many flips, 2 outcomes, count them
• Categorical → one pick, many outcomes
• Multinomial → many picks, many outcomes, count them

🧠 Callback ahead: the categorical distribution is the engine of Markov chains — "given where I am now, here are the probabilities of where I go next." You'll build those in the next tutorial.