The Concept of Chance

If we imagine a time before we had the mathematical tools to compute probability, we might be able to picture a particularly observant person noting that there were certain patterns to natural events. This person, let's call her Sharon, notices that when they sky turns a certain color it almost always means a rain storm is coming. She notices that when that particular color is in a specific region of the sky the storm is usually imminent. One summer day Sharon's family is outside enjoying the day. The day is partly cloudy, quite hot, and windy. Sharon keeps looking at the sky. During the afternoon she begins to call her children and family members together. "We'll need to head for home soon," she tells them. Not long after that, she gathers everyone up and leads them back to shelter. Almost as soon as they get home, the sky opens up and a tremendous thunderstorm is upon them. This was not an unusual occurrence for Sharon and her family. Because of her reliable "forecasts," everyone knew that when Sharon said it was time to go home, they should listen. She wasn't always correct, but she was correct often enough to have gained the attention of her family. Sharon had learned that the chance of rain was high under certain conditions. Her ability to judge the chance of rain was based on her good observation and her internalized database of past experience. If we could look into her database we would find that she possessed a sense of the quantity of rainstorms as a ratio of the number of times the sky had a specific appearance. She didn't have an actual count of the number of rainstorms, nor a count of the number of nasty-looking sky days. She didn't have a computed ratio. Therefore, we can't say that she knew the probability of a storm. She did, however, have a sense that the chance of a storm was high. Perceptive, observant people use something similar every day. The difference between this and mathematical probability is a matter of sophistication. The nature of observant, perceptive development of chance is quite at the heart of how we use probability. Mathematical probability is a formalized way of dealing with the same concept. Sharon had, and many readers of this text have, an intuitive sense for this area of mathematics. She knew that under certain conditions there was nothing to be concerned about with the weather. Under certain other conditions, she knew to keep her eye on the sky. And under other conditions she knew it was time to seek shelter. The concept at the base of each of these conditions was the concept of chance. Chance is the word we use to describe the entire range between certainty and impossibility. Probability is a mathematical measurement (or estimate) of chance.