# Short Answer Questions (submit online)

1. What is an interpretation of probability? Why does probability need an interpretation?
2. Explain the difference between a classical interpretation and a frequency interpretation of probability.
3. In what ways does the subjective interpretation of probability differ from the others?

# For Further Discussion

• Interpreting probabilistic facts. You have now seen several interesting probabilistic facts, such as 1) The law of large numbers; 2) Conditional probability; and 3) Probabilistic independence. You have also seen several interpretations of probability: 1) the classical interpretation; 2) the subjective interpretation; 3) the frequency interpretation; and 4) the propensity interpretation.
• Did you find any of these interpretations more plausible than the others? If so, why?
• These properties can be used to describe many different kinds of systems, from dice to cards to the human genome. How is it possible that such different systems share such specific mathematical properties?
• As a specific example, suppose someone asks why the average sum of a thrown pair of regular dice is 7. You might answer that it's because of the law of large numbers, and therefore because of probability theory. But suppose they asked further why these mathematical tools apply to things like dice. What could you say to such a person?
• Relatedly: if someone asks why the laws of gravity apply to both apples falling from trees and skydivers falling from airplanes, the answer might be, "Because both have mass, and the laws of gravity apply equally to all things with mass." But suppose someone were to ask why the laws of probability apply to throwing dice, dealing cards, and interpreting the human genome. How would you answer?
• The classical interpretation. The classical interpretation says that probabilities apply to sets of events of the same kind that can be reduced to cases that are equally possible, like each side of a coin in acoin toss.
• How might we flesh out what it means to be "of the same kind"?
• How about "equally possible"?
• Is possibility the kind of thing that can be treated as a matter of degree, or is everything strictly possible or impossible?