## Mutually Exclusive

### In mathematics, “mutually exclusive” refers to a situation where two events cannot occur simultaneously

In mathematics, “mutually exclusive” refers to a situation where two events cannot occur simultaneously. It means that if one event happens, the other event cannot occur at the same time.

For example, let’s consider the events of rolling a fair six-sided die and getting an even number or getting an odd number. These events are mutually exclusive because it is not possible to roll a number that is both even and odd at the same time.

Another example can be tossing a coin and getting either heads or tails. Again, these outcomes are mutually exclusive as landing on heads means it cannot simultaneously land on tails.

In general, if two events A and B are mutually exclusive, the probability of one event happening does not affect the probability of the other event occurring. Mathematically, the probability of the union of two mutually exclusive events is equal to the sum of their individual probabilities.

To illustrate this, let’s say we have two mutually exclusive events A and B. The probability of event A occurring is denoted as P(A), and the probability of event B occurring is denoted as P(B). In this case, the probability of either event A or B happening is given by the formula:

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

This formula relies on the assumption that the events A and B are mutually exclusive; otherwise, it would not hold true.

Understanding the concept of mutually exclusive events is essential in various areas of mathematics, including probability theory, statistics, and combinatorics.

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