Conditional Probability
A visual guide to understanding how new information changes probability.
Most of the time, the biggest struggle with conditional probability is distinguishing it from the probability of the intersection of two events.
At first glance, saying 27% of students are from the blue team and hate math seems the same as saying 27% of students from the blue team hate math. But they are not the same, and that is the core idea of this project.
I wanted to show that adding information changes the probability because it restricts our sample space. In the first case, the sample is the whole class. But if we know that a student was chosen from the blue team, we restrict the sample space to just that team.
The whole concept is shown through an entertaining classroom narrative, using different visual objects to aid understanding and visualization.
The conditional formula is introduced at the last stage as a natural and logical result of the idea first grasped rather than at the beginning as some kind of axiom.