Two events are said to be mutually exclusive if they cannot happen at the same time. In other words, they are said to be disjoint.
Checkout this video:
Two events are said to be mutually exclusive if they cannot happen at the same time. For example, tossing a coin and getting a head is mutually exclusive with tossing a coin and getting a tail. In other words, if you know that one of these two events has happened, then you know that the other event hasn’t happened.
In probability theory, mutually exclusive events are important because they allow us to simplify calculations. For example, when two events are mutually exclusive, we know that the probability of them both happening is zero. This means that we can simply add the probabilities of the individual events to calculate the probability of either event happening.
There are also other types of events that are not mutually exclusive, such as dependent events (where one event affects the probability of another event happening) and independent events (where the occurrence of one event does not affect the probability of another event occurring).
What are Mutually Exclusive Events?
Two events are said to be mutually exclusive if they cannot happen at the same time. For example, rolling a die and getting a 1 OR rolling a die and getting a 2 are mutually exclusive events because you cannot roll a 1 AND a 2 on the same die at the same time.
Examples of Mutually Exclusive Events
There are many examples of mutually exclusive events.
Some examples of events that are mutually exclusive are:
-Getting a head when flipping a coin
-Rolling a die and getting a 1, 2, 3, 4, 5, or 6
-Picking a card from a standard deck of cards and getting a heart, club, diamond, or spade
-Choosing a person at random and them being taller than 6 feet or shorter than 6 feet
Non-Examples of Mutually Exclusive Events
It is important to know what mutually exclusive events are in order to understand probability, but it is also helpful to know what types of events are not mutually exclusive. This will help you to better identify when two events are actually mutually exclusive.
Here are some examples of events that are not mutually exclusive:
-Getting a head when flipping a coin and also rolling a 6 on a dice.
-Choosing a black card from a deck of cards and also choosing an ace.
-Picking a yellow M&M from a bag and also picking a peanut M&M.
In conclusion, mutually exclusive events are those that cannot happen at the same time. They are usually represented by two sets of events that have no elements in common. Venn diagrams are often used to depict mutually exclusive events.