Probability

Lake Wobegon -- "where the women are strong, the men are good-looking, and all the children are above average."
--Garrison Keillor, A Prairie Home Companion
Many people believe in ESP and other paranormal phenomena because they have a poor understanding of probability.

Class Statistics

Introduction to Probability




Gambler's Fallacy




Birthday Paradox




Coin Flip Exercise

This is a simple experiment. Everyone will be given a form to use for recording results. It has 2 identical parts made up of 100 squares for recording the results of a coin toss (real or imagined). Everyone will flip a coin once to determine which part (top or bottom) of the form to use for the "brain" sequence. Record this choice in your notebook and do not write it on the form. Next - using your imagination - generate a random sequence of heads/tails (1/0) in the 100 boxes. This is the "brain" sequence. When done, flip a real coin 100 times and record the heads/tails results (as 1/0) in the other part of the form. This is the "coin" sequence. Professors Cotton and Scalise will attempt to determine which is which.


Run           
Length        Occurrences
1                 0
2                 0
3                 0
4                 6
5                11
6                 9
7                 6
8                 6
9                 3
10                1
11                1
12                0
13                0
Notice the peak at 5 to 6.



Telephone game




Clustering Illusion




Simpson's Paradox




Non-transitive Paradox




Extrapolation




Coincidence


Outline