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
Undergraduate 3757 4603 8360
Graduate 2253 4074 6327
Total 6010 8677 14687

We know that the individual is an undergraduate student so we will only look at the 8360 undergraduate students. Of those 8360 undergraduate students, 3757 were Pennsylvania residents.

\(P(PA \mid Undergrad) = \dfrac{3757}{8360}=0.449\)