The term intersection is used to describe the overlap or two or more events. This is communicated using the character ∩. The phrase \(P(A \cap B)\) is read as "the probability of A and B."
In the form of a Venn diagram, we can picture this as the overlap between two [or more] events.
Example: Cards Section
What is the probability of randomly selecting a card from a standard 52-card deck that is a red card and a king?
There are 2 kings that are red cards: the king of hearts and the king of diamonds.
\(P(red \cap king)=\dfrac{2}{52}=.0385\)
Example: Penn State Enrollment Section
The two-way contingency table below displays the Penn State's undergraduate enrollments from Fall 2019 in terms of status (full-time and part-time) and primary campus (data from the Penn State Factbook).
| Full-Time | Part-Time | Total | |
|---|---|---|---|
| University Park | 39529 | 1110 | 40639 |
| Commonwealth Campuses | 24306 | 2794 | 27100 |
| PA College of Technology | 4110 | 871 | 4981 |
| World Campus | 2574 | 5786 | 8360 |
| Total | 70519 | 10561 | 81080 |
What proportion of Penn State students were full-time University Park students?
This is an example of an intersection because we are looking for the proportion of all students who are both full-time and University Park.
\(P(FullTime \cap UniversityPark)=\dfrac{39529}{81080}=0.488\)
What proportion of Penn State students were part-time World Campus students?
This is an example of an intersection because we are looking for the proportion of all students who are both part-time and World Campus.
\(P(PartTime \cap WorldCampus) = \dfrac{5786}{81080}=0.071\)