Free Statistics Help Book
An Interactive Multimedia introductory-level statistics book.
The book features interactive demos, simulations and case studies.
Probability :  

Conditionaly Probability Demo

We recommend that you begin by answering questions before interacting with the simulation.

General Instructions

The left side shows a set of 30 objects varying in color (red, blue, and purple) and shape (X and O). One of the objects is to be chosen at random. The various possible conditional probabilities are shown below the objects. Click on one to see how the conditional probability is computed. For example, if you click on P(X|Red) which is read “the probability of X given Red” then a box is put around each of the red objects. Of these, those that are X’s are shaded. The probability of X given it is red is the number of red X’s (shaded boxes) divided by the total red items (the number of boxes).

Click “Another Example” for distribution of objects.

Step By Step Instructions

1. Pick one of the probabilities and figure out the answer yourself. Then click on the button to verify your answer.
2. Try two or three other probabilities.
3. Repeat with another example.


The conditional probability of, for example, an X given a red object is the number of red X’s divided by the number of red objects.


Begin by answering the questions, even if you have to guess. The first time you answer the questions you should not check your answers. Once you have answered all the questions, answer them again using the simulation to help you. The second time through click the “Check Answer” button to get feedback.
Copyright 2012