# 2.1.3.2.5 - Conditional Probability

Conditional Probability

The probability of one event occurring given that it is known that a second event has occurred. This is communicated using the symbol $$\mid$$ which is read as "given."

For example, $$P(A\mid B)$$ is read as "Probability of A given B."

## Example: PA Resident given Undergraduate Section

The two-way table below displays the World Campus enrollment from Fall 2019 in terms of level (undergraduate and graduate) and residency (Pennsylvania and non-Pennsylvania). Given that an individual is an undergraduate student, what is the probability that the student is a Pennsylvania resident?

Pennsylvania Non-Pennsylvania Total
$$P(PA \mid Undergrad) = \dfrac{3757}{8360}=0.449$$