Random Events and Probability

Probability starts from the plainest possible question: what outcomes can an experiment actually produce, and how likely is each one? This chapter builds the vocabulary — sample spaces and random events — then gives probability a rigorous definition and its basic properties, and closes with conditional probability, the law of total probability, and Bayes’ formula. Those last three are the machinery for reasoning backwards from evidence to cause, and every piece of statistical inference later in the course rests on them.