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It's not not accurate, it's just not complete from the perspective of modern theory. I agree that conditional probability is best demonstrated graphically. The
by nerdponx 4y ago
It's not not accurate, it's just not complete from the perspective of modern theory.
I agree that conditional probability is best demonstrated graphically. The sample space is a big rectangle, and events are represented as polygons or other closed shapes, with area proportional to their probability. Conditional probability elegantly falls out of this representation by treating one of these event-shapes as a new "sub sample space" and computing fractions of areas.
- mjburgess 4y agoYes, but it rather poisons the well against the bayesian, who says that conditional probability is basic; there are no unconditional probabilities. So this area model at once creates a lot of confusion elsewhere.
- nerdponx 4y agoI don't know. I think you need to start with the "world in a rectangle model" to build intuition. Then you can blow your students' minds with the possibility that the "rectangle" is actually the unknowably massive timeline of the entire universe, from the Big Bang until its heat death, and all of our models and reasoning are conditional on some subset of that gigantic world-rectangle. In my opinion, the power of this philosophical leap is lost without the basic geometric intuition.