# Probability

### Purpose

Provides fundamental tools for assessing risk and updating beliefs through cumulative probability calculations and Bayesian decision analysis.

### Key functions

* `ProbabilityOfAtLeastOne` — Calculates the cumulative probability of an event occurring at least once over a series of trials, with visualizations for understanding risk thresholds. 
* `ProbabilityOfHypothesisGivenData` — Implements Bayes' Theorem to update the probability of a hypothesis based on new evidence, including decision analysis to calculate the Expected Value of Information (EVOI).

### Common use cases

* **Risk Assessment**: Estimating the likelihood of a system failure, cybersecurity breach, or infection outbreak over long-term exposure.
* **Evidence-Based Decisions**: Updating clinical diagnoses or intelligence assessments as new test results or signal data become available.
* **Value of Information**: Determining if acquiring additional data (e.g., a sensor report or medical test) is financially or operationally worth the cost.
* **Strategic Reliability**: Evaluating the performance of redundant systems and long-term project risks.