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.
HOW LARGE IS PENNSYLVANIA?
Consider the area, in square miles, of Pennsylvania.
The table below lists four statements about the state's size.
PERIOD
PROBABILITY
less than 5,000 square miles
between 5,000 and 50,000 square miles
between 50,000 and 100,000 square miles
over 100,000 square miles
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.