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Events are considered mutually exclusive when they cannot happen at the same time. Imagine you have a coin and are flipping it. Getting heads and tails in one flip is impossible. This is a great example of mutually exclusive events. In probability theory, when one event like heads occurs, the event called tails cannot.
Mutually exclusive events simplify the calculation of probabilities. Instead of worrying about overlapping possibilities, you calculate the probabilities separately and add them together. It's important to understand this concept because it forms the basis for sudden intuitive leaps that make problems easier to solve.

In probability theory, rules are your best friend for understanding how likely events are. A crucial rule for mutually exclusive events states that the total probability of any number of these events occurring is the sum of their individual probabilities.
Mathematically, this is written as:

• If events \(A, B,\) and \(C\) are mutually exclusive, then \(P(A \cup B \cup C) = P(A) + P(B) + P(C)\).

It means that for events that can't happen simultaneously, calculating their combined likelihood is straightforward—just add their probabilities. This rule simplifies the computation and prevents mistakes, helping to ensure that probabilities don't accidentally overlap or exceed logical boundaries.

Understanding the limits of probability is key to getting accurate results in your calculations. Probability values must always lie within the interval from 0 to 1, inclusive. This means no event can have a probability less than 0 or greater than 1.
These limits can be thought of as the 'boundary fence' of probability. They ensure that we stay within the realm of what is mathematically and logically achievable. For example, you can't have more than 100% chance that something happens.
In the original exercise, adding up the probabilities of mutually exclusive events \(A, B,\) and \(C\) led to 1.2. This violates the probability limitations because it exceeds 1, indicating a mistake had been made in the assumptions or calculations. Staying informed about these boundaries prevents misinterpretations and helps verify the correctness of your solution.