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What are the chances? You buy a lottery ticket; what are the chances that you're going to be rich for the rest of your life?
You walk across a golf course in a stormy day; what are the chances you'll be hit by lightning?
You go to Las Vegas and you gamble your life's earnings by betting a red on roulette; what are the chances you're going to be rich?
All these examples are real examples of life situations where we're confronted with possibilities whose outcomes we do not know. In fact, I would argue that many or most parts of our lives—and the world and trying to understand the world—involve situations where we don't know what's going to happen. They involve the uncertain and the unknown.
It would be nice to say, "Well, our challenge in life is to get rid of uncertainty and be in complete control of everything." That is not going to happen. One of life's real challenges is to deal with the uncertain and the unknown in some sort of an effective way; and that is the realm of probability. Probability accomplishes the really amazing feat of giving a meaningful numerical description of things that we admit we do not know, of the uncertain and the unknown. It gives us information that we actually can act on.
Probability is a rather subtle kind of a concept because it can come out one way or the other, and still a probabilistic prediction can be viewed as correct—but decisions made on probability have all sorts of ramifications. In the case of the rain, all we risk is getting wet. But in many areas of making decisions on the basis of probability, there are very serious consequences. When we make medical decisions, for example, we are making decisions that are based on probabilities, and yet they have extremely serious consequences, including life and death consequences.
One thing that probability tries to do is to describe random phenomena. It tries to give a specific statement about what we expect when things happen at random. The reason that it can be effective at doing this is that random happenings are things where the individual outcomes of one trial or one experiment are completely unknown, but if you repeat them many, many times, or you look at them in the aggregate, they have some regularity to them; and so the amazing accomplishment of probability is to put a meaningful numerical number value on the things that we admit we don't know.
One of the challenges for this course is to understand what to expect from randomness, and that is the role of probability: to describe what to expect from random phenomena. The goal of probability is to give a numerical measure of those chances. We're going to then see a myriad of applications, by the way, of probability in all sorts of things, from games, to science, to business, and many other parts of life.