Probability Topics
Probability measures how likely an event is to occur. This chapter introduces the terminology of probability, explains what it means for events to be independent or mutually exclusive, presents the addition and multiplication rules for combining probabilities, and shows how contingency tables, Venn diagrams, and tree diagrams organise and display them.
Terminology of Probability
Probability is a number between zero and one that measures how likely an event is to happen, where zero means impossible and one means certain. An experiment is a process with an uncertain result, the sample space is the set of all possible outcomes, and an event is any collection of outcomes. The probability of an event is the proportion of outcomes that make it up when outcomes are equally likely, and the probabilities of all outcomes in the sample space add to one.
Independent and Mutually Exclusive Events
Two events are independent if the occurrence of one does not change the probability of the other, such as separate coin tosses. Two events are mutually exclusive if they cannot both happen at the same time, so they share no outcomes. These are different ideas: mutually exclusive events are strongly related, because one occurring rules the other out, whereas independent events have no influence on each other at all. Deciding which relationship holds determines how their probabilities combine.
Rules and Diagrams
The addition rule finds the probability that one event or another occurs, subtracting the overlap so it is not counted twice. The multiplication rule finds the probability that two events both occur, using conditional probability when the events are dependent. Contingency tables organise counts across two variables, Venn diagrams show how events overlap, and tree diagrams lay out sequences of outcomes with their probabilities, each making it easier to apply the rules correctly.