Mr. Rogers - AP Statistics

Independent Events

Conditional Events

The Relationship of Venn Diagrams to Tree Diagrams--Independent Events

Any probability problem that can be represented by a Venn diagram can also be represented by a tree diagram and vice versa. The diagrams at right are set up for independent events, but will look very similar for independent events.

Note that specific leaves on the tree correspond to specific areas of the Venn diagram. This is true for both independent and conditional events.

For Independent Events:

The relationships below show how the tree diagram for 2 independent events is related to the diagram for 2 conditional events. Note that for independent events, the second set of branches are identical regardless of whether event A is or isn't true. This is not the case for conditional events.

P(B) = P(B|A) = P(B|AC)
  1. P(A∩B) = P(A) P(B)
  2. P(AUB) = P(A) + P(B) - [P(A) P(B)]

For conditional events, non of the above relationships will be met.


  • P(A)  =  49 %, probability of being male
  • P(B)  =  20 %, probability of blue eyes
  1. P(A∩B) = 9.8 %, probability of  being a male and having blue eyes
  2. P(AUB) = 59.2 %, probability of being a male or having blue eyes




< Return to Unit Plan



SAM Team--Southside High School's STEM and Computer Science extra-curricular club (Mr. Rogers Sponsor)

Mr. Rogers' Twitter Site

Mr. Rogers Teacher's Blog

Mr. Rogers T-shirts

Mr. Rogers Information for Teachers

Mr. Rogers Science Fair Information

Check out other web sites created by Mr. R:

Check out Articles by Mr. Rogers:

Insultingly Stupid Movie Physics is one of the most humorous, entertaining, and readable physics books available, yet is filled with all kinds of useful content and clear explanations for high school, 1st semester college physics students, and film buffs.

It explains all 3 of Newton's laws, the 1st and 2nd laws of thermodynamics, momentum, energy, gravity, circular motion and a host of other topics all through the lens of Hollywood movies using Star Trek and numerous other films.

If you want to learn how to think physics and have a lot of fun in the process, this is the book for you!


First the web site,

now the book!

Mr. Rogers Home | Common Sylabus | AP Comp Sci I | AP Comp Sci II | AP Physics Mech | AP Physics E&M | AP Statistics | Honors Physics|IB Design Tech | Southside

[ Intuitor Home | Physics | Movie Physics | Chess | Forchess | Hex | Intuitor Store |

Copyright 1996-2011 T. K. Rogers, all rights reserved. Forchess is a registered trademark of T. K. Rogers.
No part of this website may be reproduced in any form, electronic or otherwise, without express written approval.