Event Probability P(A) & Axiomatic Sample SpaceDimensionless Real Ratio [0.000000, 1.000000]
The fundamental measure of likelihood that a specific event occurs within a defined sample space S. Governed by the Kolmogorov Axioms: non-negativity P(A) >= 0, unitarity P(S) = 1, and additivity for mutually exclusive events. Expressed identically as a decimal between 0 and 1, a percentage between 0% and 100%, or an irreducible integer ratio of favorable outcomes to total equally likely outcomes.
Default: 0.5000 (50.0%)
Joint Probability P(A and B) & Stochastic IndependenceJoint Set Measure [0.000000, 1.000000]
The probability of both event A and event B occurring simultaneously in a single trial or composite experiment. If events are independent, P(A intersect B) = P(A) * P(B). If dependent, P(A intersect B) = P(A) * P(B|A). The value is strictly bounded above by min(P(A), P(B)) and below by max(0, P(A) + P(B) - 1) according to Frechet inequalities.
Default: 0.0833 (8.33%)
Union Probability P(A or B) & Inclusion-ExclusionUnion Set Measure [0.000000, 1.000000]
The likelihood that at least one of the events occurs. Computed via the Principle of Inclusion-Exclusion: P(A union B) = P(A) + P(B) - P(A intersect B). When events are mutually exclusive (disjoint), the intersection term vanishes, simplifying to direct summation P(A) + P(B).
Default: 0.5833 (58.33%)
Conditional Probability P(A|B) & Bayesian LikelihoodNormalized Subspace Probability [0.000000, 1.000000]
The updated probability of event A occurring given that event B is known to have already occurred: P(A|B) = P(A intersect B) / P(B), where P(B) > 0. In Bayesian analysis, this represents the posterior probability after updating prior beliefs P(A) with the observed empirical likelihood P(B|A).
Default: 0.5000 (50.0%)
Odds in Favor (X:Y) & Odds AgainstCoprime Integer Ratio / Relative Likelihood
The ratio of the probability that an event occurs to the probability that it does not occur: Odds in Favor = P(A) / (1 - P(A)). A 75% probability corresponds to odds in favor of 3 to 1 (3:1). Odds against represent the reciprocal ratio (1 - P(A)) / P(A), universally employed in gaming and contract underwriting.
Default: 1:1 (Even Odds)
Bernoulli Trial Count (n) & Target Successes (k)Discrete Repetition Count (n >= 1, 0 <= k <= n)
Parameters governing binomial experiments consisting of n independent and identically distributed (i.i.d.) trials, each with constant binary success probability p. Combinatorial combinations C(n, k) determine the total permutations yielding exactly k successes.
Default: n = 10 trials, k = 5 successes
Bayes Base Rate Prior P(Hypothesis)Prevalence Baseline Proportion [0.000001, 1.000000]
The initial baseline probability of an event or medical condition before incorporating diagnostic test evidence. Ignoring this base rate leads to the Base Rate Fallacy, wherein high-accuracy tests yield paradoxically low positive predictive values when screening rare phenomena.
Default: 0.0010 (0.1% Prevalence)
