Basic Ideas in Probability

Abstract

We will perform experiments—which could be pretty much anything, from flipping a coin, to eating too much saturated fat, to smoking, to crossing the road without looking—and reason about the outcomes (mostly bad for the examples I gave). But these outcomes are uncertain, and we need to weigh those uncertainties against one another. If I flip a coin, I could get heads or tails, and there’s no reason to expect to see one more often than the other. If I eat too much saturated fat or smoke, I will very likely have problems, though I might not. If I cross the road without looking, I may be squashed by a truck or I may not. Our methods need also to account for information. If I look before I cross the road, I am much less likely to be squashed. Probability is the machinery we use to describe and account for the fact that some outcomes are more frequent than others.