Probability theory formalizes the analysis of random experiments through a sample space (the set of all possible outcomes, each fully specifying every random choice made), a probability function assigning each outcome a value between 0 and 1 such that all outcomes sum to 1, and events defined as subsets of the sample space whose probability is the sum of the probabilities of their constituent outcomes. The tree method constructs the sample space systematically by branching on each random choice in sequence and assigns each outcome's probability as the product of the conditional probabilities along its path, correctly weighting non-uniform outcome likelihoods rather than assuming naive equal-likelihood counting. This methodology belongs to discrete probability theory and demonstrates that correct probabilistic reasoning, grounded in explicit sample-space construction and stated assumptions, can produce results that contradict strong human intuition, including cases where a relation (such as one outcome "beating" another) fails to be transitive.
Probability theory formalizes the analysis of random experiments through a sample space (the set of all possible outcomes, each fully specifying every random choice made), a probability function assi…