\(\renewcommand{\P}{\mathbb{P}}\)

Simple Probability Experiment

Sample Space
Event Prob Rel Freq
\( \emptyset \)
\( A \)
\( B \)
\( A^c \)
\( B^c \)
\( A \cap B \)
\( A \cup B\)
\( A \cap B^c \)
\( B \cap A^c \)
\( A \cup B^c \)
\( B \cup A^c \)
\( A^c \cap B^c \)
\( A^c \cup B^c \)
\( (A \cap B^c) \cup (B \cap A^c) \)
\( (A \cap B) \cup (A^c \cap B^c) \)
\( S \)
Points  

Description

In this app, \(A\) and \(B\) are rectangular events in a rectangular sample sapce \(S\). The sample space \( S \) is given the uniform distribution, so \( \P(E) = \text{area}(E) \big/ \text{area}(S) \) for every event \( E \). Events \( A \) and \( B \) can be moved by dragging an interior point of the rectangle, or resized by dragging the lower right corner of the rectangle. The first column of the tables gives the 16 events that can be constructed from \(A\) and \(B\) using the basic set operations of union, intersection, and complement. The probabiliy of each event is given in the second column. Click on an event in the list to see the selected event colored blue in the Venn diagram. When the experiment runs, the outcomes (elements of \( S \)) are shown as red dots. The relative frequency of each event is given in the third column of the table.