Which type of probability allows distribution of events to be inferred without collecting data?

The type of probability that allows distribution of events to be inferred without collecting data is theoretical probability. This concept is grounded in the mathematical principles of probability and is based on the reasoning of equally likely outcomes. Theoretical probability relies on established models and assumptions about random processes, enabling predictions about the likelihood of events occurring purely through logical deduction rather than empirical observation.

In scenarios where events can be precisely defined and their potential outcomes understood (such as rolling a fair die or flipping a fair coin), theoretical probability provides a framework to calculate the likelihood of different outcomes. For instance, the theoretical probability of rolling a three on a six-sided die is 1 in 6, derived mathematically rather than observed through actual rolls.

Contrarily, relative frequency probability is based on observed data and calculated as the ratio of the number of times an event occurs to the total number of trials. Empirical probability also involves data collection, reflecting the actual outcomes of past events. Classical probability, while sometimes associated with scenarios similar to theoretical probability, often implies a narrower focus on situations where outcomes are equally likely, which is a subset of theoretical reasoning.

Thus, theoretical probability stands out as the approach that allows inference about events without needing direct data collection.