How is p(A) most accurately defined?

The probability p(A) is defined as the marginal probability of event A. Marginal probability refers to the likelihood of a single event occurring without consideration of other events or conditions. It is calculated by summing or integrating the joint probabilities of event A across all relevant scenarios.

In this context, p(A) gives us insight into how probable event A is within the entire sample space, independent of any other factors that may affect its occurrence. For instance, if we are analyzing the probability of a patient developing a certain condition, p(A) allows us to understand the risk associated with that condition based solely on the broader population data. This concept is foundational in probability theory and is often used in statistical analyses, including in healthcare statistics, where understanding individual event probabilities can inform risk assessments and decision-making processes.

The other options do not accurately represent the definition of p(A). The joint probability indicates the likelihood of two or more events happening simultaneously, while proof refers to a logical validation of a statement rather than a probability measure. Lastly, mentioning the marginal probability of an event not occurring is a distinct concept and does not pertain to defining p(A) itself.