Flip a quarter a hundred times. What's the probability that it will turn up heads? Tails? Even if we are unsure about whether something will happen, can we start to be mathematical about the "chances" of an event (essentially realizing that some things are more likely than others) occurring. This tutorial will introduce us to the tools that allow us to think about random events and the logic behind comparing, judging, and finding the probabilities of those events.
When we are trying to make a judgement about a population, it is often impractical (or impossible) to observe every member of the population. Imagine trying to survey all 300+ million Americans to understand the likely outcome of the next presidential election! Because of this, much of statistics is collecting data from a representative and random sample. From the data collected from this random sample we can infer things about the greater population.