Probability Topics

Summary :

This chapter introduces the vocabulary and systematic methods of probability, from the everyday intuition used when weighing whether to study for an exam to the formal terminology of experiments, outcomes, and events. It covers sample spaces, the notation for events and their probabilities, and distinguishes independent from mutually exclusive events.

Everyday intuition and formal terminology

The chapter starts from the observation that decisions ranging from a politician's campaign strategy to a doctor's choice of treatment already rely on an intuitive sense of probability, then formalizes this by defining an experiment as a planned operation carried out under controlled conditions and a chance experiment as one whose result is not predetermined.

Sample spaces, outcomes, and events

A result of an experiment is called an outcome, and the sample space, denoted S, is the set of all possible outcomes, which can be represented by listing them, by a tree diagram, or by a Venn diagram; an event is any combination of outcomes and is written with an upper-case letter, with its probability denoted P of that letter.

Independent and mutually exclusive events

The chapter draws a careful distinction between events that are independent, where the occurrence of one does not affect the probability of the other, and events that are mutually exclusive, which cannot occur together, a distinction the chapter stresses is not the same relationship despite the two terms sometimes being confused.