Distributionsthe shape of chance
Every outcome gets a probability; the whole picture is a distribution, and its shape tells you what to expect.
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Roll two dice and add them. The sum lands somewhere between two and twelve — eleven possible outcomes, but they are not equally likely. A seven can happen six ways out of the thirty-six possible rolls; a twelve needs double sixes — just one way. So give every outcome a bar, and let each bar's height be its probability.
That whole picture has a name: a distribution — a set of probabilities, one for every possible outcome. And it obeys a single rule: stack the probabilities up, and together they reach exactly one. Some sum has to come up, so the bars share the whole of chance between them.
And the shape tells a story. Trace the outline of the bars: a triangle, peaking at seven. Middle sums are common, because many different pairs of faces make them. Extreme sums are rare — only snake eyes makes a two, only double sixes makes a twelve. Before the dice even land, the shape says: expect something near seven.
Different situations draw different shapes. A single fair die: each face has the same chance, one sixth, so every bar matches — the shape is flat. A loaded die, weighted toward six: nearly all the probability piles onto one spike. Both are honest distributions — each still has to add to one — but they tell opposite stories: total suspense, or almost none.
So that is a distribution: chance drawn as a picture. List every outcome, give each its share of probability, and make the shares add up to one. Then read the shape. A triangle says expect the middle. A flat line says anything goes. A spike says it is all but decided. The shape tells you what to expect before anything has happened.