Overview
On this page, we discuss the notion of conditional probability, one of the key ideas in the theory of probability.
Basic learning objectives
These are the tasks you should be able to perform with reasonable fluency when you arrive at your next class meeting. Important new vocabulary words are indicated in italics.
 Calculate conditional probabilities for events in sample spaces where all outcomes are equally likely by reducing the sample space.
Advanced learning objectives
In addition to mastering the basic objectives, here are the tasks you should be able to perform after class, with practice:

Calculate conditional probabilities more generally by using the formal definition of conditional probability.

Calculate the probability of two events both occurring by using the intersection law derived form the definition of conditional probability.

Understand that the Kolmogorov axioms apply after conditioning on any event A with nonzero probability, and hence all probability laws and rules we’ll derive still apply to events conditioned on A.
To prepare for class

Watch the following video which introduces the notion of a conditional probability.

Watch the following video (by jbstatistics) which discusses the definition of conditional probability:
After class

Watch the following video (by jbstatistics) which shows some examples of calculating conditional probabilities (note that he already mentions the concept of independent events, which we will discuss later):