What statistical formula determines the probability of an event based on prior conditions?

Bayes' theorem is fundamental in statistics for calculating the probability of an event based on prior knowledge or conditions. It essentially allows for the updating of the probability of a hypothesis as more evidence becomes available. This theorem is particularly powerful in scenarios where previous data or outcomes can inform the likelihood of current or future events, making it valuable in fields such as machine learning, decision-making, and predictive modeling.

The theorem incorporates prior probabilities and likelihoods to produce a posterior probability, reflecting how new information may alter the initial assumptions. In practical terms, if we know the probability of a condition being true (prior), along with the likelihood of the observed data under that condition, Bayes' theorem helps in determining the probability of the condition given the data (posterior).

The other options, while important in statistics, serve different purposes. Regression analysis focuses on modeling relationships between variables, variance analysis measures how data points differ from each other, and statistical significance testing evaluates whether observed data can be attributed to random variation. None of these options specifically address the role of prior conditions in determining the probability of an event in the dynamic manner that Bayes' theorem does.