- Disjoint & Independent Events

Disjoint events and independent events are different. Events are considered disjoint if they never occur at the same time; these are also known as mutually exclusive events. Events are considered independent if they are unrelated.

Disjoint Events Section

Disjoint events are events that never occur at the same time. These are also known as mutually exclusive events

These are often visually represented by a Venn diagram, such as the below. In this diagram, there is no overlap between event A and event B. These two events never occur together, so they are disjoint events.

Mutually Exclusive

Example: First-Year & Sophomore Students Section

Let's consider undergraduate class level. A student can be classified as a first-year student, sophomore, junior, or senior.

Being a first-year student and being a sophomore are disjoint events because an individual cannot be classified as both at the same time. 

Independent Events Section

Independent events are unrelated events. The outcome of one event does not impact the outcome of the other event. Independent events can, and do often, occur together. 

The following examples use stacked bar charts to demonstrated what two variables that are and are not independent look like in relation to one another. 

Example: Penguin Species & Biological Sex Section

Stacked bar chart of Penguins' species and biological sex

The segmented bar chart above displays data from a research study concerning penguins (see Palmer Penguins). Within each of the three species of penguin, half of the penguins are male and half are female. In this sample, penguin species and biological sex are independent. Knowing the species of a penguin does not change the probability that they are male or female. And, knowing the biological sex of a penguin does not change the probability that it is an Adelie, Chinstrap, or Gentoo penguin.

Non-Example: Enrollment Status by Campus Section

Stacked bar chart of Penn State enrollment by status and campus

The segmented bar chart above displays data concerning Penn State students' status as full- or part-time and their primary campus (data from Penn State's Factbook). The proportion of students who are part-time is different at each campus. Only 2.7% of University Park students are enrolled part-time while 69.2% of World Campus students are enrolled part-time. Enrollment status and primary campus are not independent. If we know a student's campus, that changes the probability of them being a full- or part-time student. If we know that a student is full- or part-time, that chances the probability that they came from a specific campus.