If you have a situation where you need to find the combined probability of overlapping events, which rule applies?

In the context of probability, when dealing with overlapping events, the addition rule is what you would use to find the combined probability. This rule helps in calculating the probability of the occurrence of at least one of two overlapping events.

Specifically, when you have two events A and B that can occur simultaneously, the addition rule states that the probability of either event A or event B occurring can be determined by adding the probabilities of A and B individually and then subtracting the probability of both events occurring together. Mathematically, this is expressed as:

P(A or B) = P(A) + P(B) - P(A and B)

This formula is essential in ensuring that the overlap (the probability of both events occurring) is not counted twice. This clearly shows why the addition rule is applicable when addressing the situation of overlapping events.

The other concepts mentioned, like the multiplication rule and conditional probability, serve different purposes in probability theory. The multiplication rule is for determining the probability of independent events happening together, while conditional probability focuses on the probability of an event occurring given that another event has already occurred. Bayes' Theorem is a method for updating probabilities based on new evidence and is not specifically about combining the probabilities of overlapping events.