lowprobability

Low probability refers to events or outcomes that have a small likelihood of occurring, as measured by a probability value between 0 and 1. What counts as low is context dependent; for a large-scale process, even probabilities on the order of 10^-3 or 10^-4 can be considered very low, while in other settings a higher threshold might apply.

In probability theory, a discrete event with probability p has p equal to the ratio of favorable outcomes to the total number of possible outcomes. In continuous models, the probability of a single exact value is zero; instead, probabilities are assigned to ranges via a probability density function and obtained by integrating over an interval, yielding a cumulative probability between 0 and 1.

Low probability is often discussed in relation to risk and decision making. An event with a small probability can still have significant consequences, especially if the outcome is costly or dangerous. This is the focus of discussions around low-probability, high-impact events, sometimes called tail risks or black swan events in popular discourse. Modeling approaches to such events include tail analysis, extreme value theory, and heavy-tailed distributions, which seek to estimate the likelihood of rare outcomes more accurately than standard models.

Common misinterpretations include assuming that a low probability makes an event impossible, or equating a low probability with low importance. In statistical practice, probabilities inform expectation and decision rules, but they do not alone determine outcomes in any single trial. Bayesian and frequentist perspectives offer different philosophical interpretations of probability, yet both quantify low probability in comparable numerical terms.