Mutually Exclusive Events Definition
Two events are said to be mutually exclusive if they can’t occur simultaneously. In other words, mutually exclusive events are called disjoint events. If two events are considered disjoint events, then the probability of both events occurring at the same time is zero.
Examples of Mutually Exclusive Events
Some examples of mutually exclusive events are,
- Tossing a coin we either get a head or a tail. Head and tail cannot appear simultaneously. Therefore, the occurrence of a head or a tail is two mutually exclusive events.
- In throwing a die all the 6 faces numbered 1 to 6 are mutually exclusive as if any one of these faces comes on the top, the possibility of others in the same trial is ruled out.
Dependent and Independent Events
An event in probability falls under two categories,
- Dependent Events
- Independent Events
Dependent Events: We define two events as dependent events if the occurrence of one event changes the probability of another event. For example, tossing a coin if we get a tail we can never get a head in the same trial.
Independent Events: We define two events as independent events if the occurrence of one event does not change the probability of another event. For example, taking a card from a well-shuffled deck can be either a face card or a black card or both here all the events are independent events. We can also say that independent events are never mutually exclusive events.
Learn More about Dependent and Independent Events
Mutually Exclusive Events
We define mutually exclusive events as events that can never happen simultaneously, i.e. happening an event rules out the possibility of happening the other event. Suppose a cricket match between India and Pakistan can result in the winning of any one team and the loss of the other team both teams can never win the match simultaneously, i.e. if Pakistan wins the match then India definitely loses the match and if India wins the match Pakistan definitely loses the matches thus, we can say Winning of India and Winning of Pakistan both are mutually exclusive events. And occurring one event definitely rules the probability of the other event.
Let’s learn more about mutually exclusive events, their formula, the Venn diagram, and others in detail in this article.
Table of Content
- Mutually Exclusive Events Definition
- How to Calculate Mutually Exclusive Events?
- Probability of Mutually Exclusive Events OR Disjoint Events
- Mutually Exclusive Events Venn Diagram
- Mutually Exclusive Events Probability Rules
- Conditional Probability for Mutually Exclusive Events