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Ladder

Bayes — the ladder

2 distinct arguments against one idea, from the one that introduces it to the one that assumes the rest.
  1. Bayes' theorem as two rectangles. A unit square split by how common the condition is (1.0%) and then by how the test behaves. Of everyone who tests positive, the fraction who have it is 16.7%.

    Bayes' theorem is a picture of a square

    A test that is 99% accurate returns a positive result. The chance it is right can easily be under one in five, and the reason is visible the moment the population is drawn as a square rather than described as a formula.

    rung 1 · probability
  2. Three doors, as areas. Staying wins 33.3% of the time and switching wins 66.7%, because the host's choice is constrained by what the host can see, so opening a door rules a region out without moving any boundary.

    The door that was not opened

    Three doors, one prize, a host who opens a losing door and offers a swap. Switching wins two times in three, and the reason is not about doors — it is about what the host was allowed to do.

    rung 2 · probability

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