# Mutually exclusive vs not mutually exclusive

## What is the difference between mutually exclusive and not mutually exclusive?

The key difference between mutually exclusive and not mutually exclusive is that mutually exclusive events cannot happen at the same time while not mutually exclusive events can happen simultaneously.

Mathematically, two events are said to be mutually exclusive if they cannot happen simultaneously. In other words, if one event happens, the other event cannot happen. For example, getting a head and a tail in a coin toss are mutually exclusive events because only one can happen at a time. On the other hand, two events are said to be not mutually exclusive if they can happen at the same time. For example, getting a head and getting a number greater than 5 in a dice roll are not mutually exclusive events because they can happen simultaneously.

## How do you know when something is mutually exclusive?

If two things are mutually exclusive, it means that they cannot happen at the same time. For example, you cannot be in two places at once, so being in New York and being in Los Angeles are mutually exclusive events.

However, not all events are mutually exclusive. It is possible to be both happy and sad at the same time, for example. In fact, many events that we experience are not mutually exclusive.

## What are some examples of mutually exclusive events?

Two events are said to be mutually exclusive if they cannot happen at the same time. For example, getting an ‘A’ in math and getting a ‘D’ in math are mutually exclusive. They cannot happen at the same time because you can only get one grade on an exam.

Other examples of mutually exclusive events can be found in everyday life. For example, you cannot be both pregnant and not pregnant. It is one or the other, but not both. Another example is being employed and unemployed – you cannot have both of those statuses at the same time.

Not all events are mutually exclusive, however. For example, two people can both be employed and have a college degree. It is possible to have more than one event happen simultaneously. These types of events are not mutually exclusive.

## What are some examples of events that are not mutually exclusive?

There are many examples of events that are not mutually exclusive. For instance, two events can both occur simultaneously, such as a coin landing on heads and tails at the same time. Alternatively, two events could be dependent on each other, such as drawing a king from a deck of cards and then choosing the next card to be an ace. Two events can also be independently likely or unlikely to occur, such as drawing a king from a deck of cards and then choosing the next card to also be a king.