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Chapter 2
Counting outcomes
Before any probability, one question: what exactly are the outcomes? Most probability mistakes are counting mistakes in disguise.
1
Leibniz's mistake
The great mathematician Leibniz once argued that with two dice a sum of 11 is exactly as likely as a sum of 12, because each can be made only one way: 5 + 6 and 6 + 6. Here are all the outcomes of two dice, one cell per pair. Tap every cell with a sum of 11 or 12.