I. Intro
In probability, a Venn diagram is a graphic organizer that shows a visual representation for all possible outcomes of an experiment and the events of the experiment in ovals. Normally, in probability, the Venn diagram will be a box with overlapping ovals inside. Look at the diagram below:
Example
Sample Space (S)
The Sample Space (𝑆) represents all of the possible outcomes of a random experiment.
Events
The ovals (in this example 𝐴 and 𝐵) are referred to as events. An event is a subset of the sample space, representing one or more possible outcomes of a random experiment.
Outcome
A single result of an experiment.
Two coins are tossed one after the other. Event A consists of the outcomes when tossing heads on the first toss. Event B consists of the outcomes when tossing heads on the second toss. Draw a Venn diagram to represent this example.
We know that:
Notice that event A and event B share the Heads + Heads outcome and that the sample space contains Tails + Tails, which is neither in event nor event.
II. Intersection & Union
We know that:
Notice that event A and event B share the Heads + Heads outcome and that the sample space contains Tails + Tails, which is neither in event nor event.
II. Intersection & Union
Event A represents randomly choosing a student from High School who holds a part-time job. Event B represents randomly choosing a student from High School who is on the honor roll. Draw a Venn diagram to represent this example.
We know that:
Notice that the overlapping oval for A and B represents the students who have a part-time job and are on the honor roll. The sample space, S , outside the ovals represents students neither holding a part-time job nor on the honor roll.
In a Venn diagram, when events A and B occur, the symbol used is ∩. Therefore, A∩B is the intersection of events A and B and can be used to find the probability of both events occurring. In this example the intersection of A & B are the students both holding a part-time job and that are on the honor roll.
We know that:
Notice that the overlapping oval for A and B represents the students who have a part-time job and are on the honor roll. The sample space, S , outside the ovals represents students neither holding a part-time job nor on the honor roll.
In a Venn diagram, when events A and B occur, the symbol used is ∩. Therefore, A∩B is the intersection of events A and B and can be used to find the probability of both events occurring. In this example the intersection of A & B are the students both holding a part-time job and that are on the honor roll.
If, in a Venn diagram, either A or B occurs, the symbol is ∪. This symbol would represent the union of events A and B , where the outcome would be in either A or B. In this example, the union of A & B would be the students that are holding a part-time job or that are on the honor roll.
Intersection
The intersection of events A and B, denoted A ∩ B, includes only the outcomes common to both A and B, representing "A and B" occurring together.Intersection
Union
The union of two events A and B, denoted A ∪ B, consists of all outcomes that belong to A, or B, or both.
Example
You are asked to roll a die. Event A is the event of rolling a 1, 2, or a 3. Event B is the event of rolling a 3, 4, or a 5. Draw a Venn diagram to represent this example. What is A∩B? What is A∪B?
https://flexbooks.ck12.org/cbook/ck-12-basic-probability-and-statistics-concepts/section/1.1/primary/lesson/venn-diagrams-bsc-pst/
https://www.siyavula.com/read/za/mathematics/grade-11/probability/10-probability-01
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