A condensed summary of probability∗

some operations on these things. • The universe is the set of all possible results. Sometimes, the universe can be big (like all of English), or even infinite. Sometimes the universe can be small, like when you are flipping a coin: then, it just contains “heads ” and “tails”. • The number is an extension of a Boolean truth value. Zero corresponds to false, one corre-sponds to true, and everything in between corresponds to degrees of uncertainty. • The constraint matches the logical law of the excluded middle: the probabilities of all the alternatives sum to one. • The arithmetical operations correspond to the standard logical operations of Boolean logic. If you use the right arithmetic and meet the other three requirements, you have a probability, and you can reproduce all results of Boolean logic by using probabilities of zero or one. Consequently, probabilities form a system of logic that is a generalisation of Boolean logic. 2 What to Ignore • There are two alternative interpretations of probabilities, which are called “Subjective ” and “Frequentist. ” Ignore the difference: they are not mutually exclusive and one gets the same answers either way. • People can be divided into “Bayesian ” or “non-Bayesian”, which refers to their attitudes toward a subjective interpretation of probability and their willingness to use Bayes ’ Theorem. Don’t bother dividing: it’s a psychological divide, not a mathematical one. ∗This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License. To view a copy of this license, visi