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Understanding the concept of probability is essential in the study of events and outcomes within mathematics. At its core, probability measures the likelihood of an event occurring. It is a numerical value between 0 and 1 where 0 indicates impossibility, and 1 indicates certainty. The basic formula for probability is:

\[ P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \]
When dealing with non-mutually exclusive events, the calculation of probability requires an adjustment to account for the fact that some events might happen together. Remember, if you can simultaneously achieve both Event A and B, then the individual probabilities of A and B aren't enough to give us the full picture. We also need to consider their intersection, which is when both events happen at the same time.

Mutually exclusive events are the bread and butter of basic probability. They refer to events that cannot happen at the same time. For example, when flipping a standard coin, it can only land on either heads or tails, not both simultaneously. That makes these outcomes mutually exclusive. However, if events are not mutually exclusive, like drawing a red card or a face card from a standard deck, they can both occur as a card can be both red and a face card.

In terms of calculating probabilities, when events are mutually exclusive, the probability of either event happening is simply the sum of their individual probabilities. But remember, this is only true when the events can't occur at the same time.

Combinatorics is the field of mathematics dedicated to counting, arranging, and describing structures within a set. When relating combinatorics to probability, it's about finding the number of ways certain outcomes can occur, which directly relates to the favorable outcomes in a probability expression.

For instance, in the case of rolling a die and looking for a number less than 5, there's a combinatoric approach to determine how many outcomes (1 through 4) qualify as 'favorable' out of the total six possible outcomes. Understanding the principles of combinatorics allows us to better grasp the concept of non-mutually exclusive events, since we can count the number of occurrences where two events can happen together.

Basic statistics come into play when analyzing events and their probabilities, especially when we need to describe, organize, and interpret those numbers. It includes concepts like mean, median, and mode, as well as more complex ideas such as variance and standard deviation. To relate it to our discussion on non-mutually exclusive events, statistics would help us understand the average rate of occurrence for these events, and how they deviate from the norm.

In practice, if we repeatedly observe the rolling of a die and the flipping of a coin, basic statistics could tell us the frequency of rolling a number less than 5 and flipping heads out of a large number of tries. Thus, providing a practical perspective on the theoretical probabilities calculated.