ABSTRACT
What is the probability that a randomly drawn card from a well-shuffled standard deck would be a heart? What is the probability that the German soccer team will win the next world championships?
These two questions are quite different. In the first, we can develop a mathematical theory from the assumption that each card is equally likely. If there are 13 cards each of hearts, diamonds, spades, and clubs, we calculate that the probability of drawing a heart is 13/52, or 1/4. We test this theory by repeating the experiment again and again. After a great deal of evidence (that 25% of the draws are hearts), we have confidence in using this model of past data to predict the future.
