# 2.1.3.2.2 - Intersections

2.1.3.2.2 - Intersections

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

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

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 39529 1110 40639 24306 2794 27100 4110 871 4981 2574 5786 8360 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.

$$P(PartTime \cap WorldCampus) = \dfrac{5786}{81080}=0.071$$

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