## 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?

1. 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.