ACTIVITY  CHANGING PROBABILITIES WHEN NEW INFORMATION IS AVAILABLE
(from DeGroot, 1970)
The point of this activity is to demonstrate that probabilities that we
assign are conditional on our current knowledge. As we learn and gain
more information, our probabilities about statements can change.
Later, we will introduce a formula, Bayes' rule, which will tell us
how to compute new probabilities when we get information.
WHEN WAS JOHN TYLER BORN?

Consider the year of birth of John Tyler, former President of the United States.
The table below lists four statements about Tyler's year of birth.
YEAR OF BIRTH 
PROBABILITY 

no later than 1750  
between 1751 and 1775  
between 1776 and 1800  
after 1800  
 Which of the four statements do you believe is most likely?
 Which of the statements do you believe is least likely?
 Give probabilities to the four events that are consistent
with the answers you made above. Put your answers in a probability table
like shown above.

You are now given the information that John Tyler was the tenth
president of the United States. Use this information to reevaluate
the probabilities you made above. Before you assign probabilities,
answer the first two questions stated above.

You are now given the information that George Washington, the first
President of the United States, was born in 1732. Again reevaluate
your probabilities and answer all three questions.

You are now given the information that John Tyler was inagurated as
President in 1841. Answer the same three questions.
Page Author: Jim Albert (© 1996)
albert@bayes.bgsu.edu
Document: http://wwwmath.bgsu.edu/~albert/m115/probability/tyler4.html
Last Modified: November 24, 1996