This exercise was inspired by the article "Quantifying Probabilistic Expressions" by F. Mosteller and C. Youtz in Statistical Science, February 1990.

In this exercise, you will associate words that represent uncertainty with numerical probabilities. I would also like you to think of an event corresponding to each combination of words and probabilities.

For example, I think you will agree that the word "never" is associated with a probability of zero. An example of an event that corresponds to "never" might be "Saddam Hussein will never be President of the United States."

Here is a list of words and phrases that represent uncertainty. Feel free to add to it if you can think of others.

Occasionally   Often         Likely      Almost Always  Once in a While
Sometimes      Rarely        Unlikely    Possible       Probable
Frequently     Infrequently  Usually     Unusually      Improbable

Tasks

1. Put the words and phrases in order of meaning from least likely to most likely.

2. Assign a scale of numerical probabilities to the words in the list.

   Note: You may not use the values 0 and 1 for any of the words!

3. Write down an event from your knowledge or experience to match to each word/probability pair.

4. Place each of the following events on your probability scale by associating it with a word/probability pair (or by placing it in between two word/probability pairs).
   A randomly selected undergraduate student at IUP will take more than four years to finish his or her degree.

   An effective treatment for AIDS will be discovered in your lifetime.

   A cure for cancer will be discovered in your lifetime.

   What is the probability of guilt at the beginning of a trial, when the defendant is "innocent until proven guilty?"

   What threshold is the probability of guilt required to surpass for a defendant to be guilty "beyond a reasonable doubt?"