Introduction

The General Idea. The basic ideas behind probability theory are as simple as those associated with making lists-the prospect of computing probabilities or thinking in a ‘probabilistic’ manner should not be intimidating. Conceptually, the steps required to compute the chance of any particular event are as follows.

• Define an experiment and construct an exhaustive description of its possible outcomes.

• Determine the relative likelihood of each outcome.

• Determine the probability of each outcome by comparing its likelihood with that of every other possible outcome.

We demonstrate these steps with two simple examples. In the first we consider three tosses of an honest coin. The second example deals with the rainfall in winter at West Glacier in Washington State (USA).

Simple Events and the Sample Space. The sample space, denoted by S, is a list of possible outcomes of an experiment, where each item in the list is a simple event, that is, an experimental outcome that cannot be decomposed into yet simpler outcomes. For example, in the case of three consecutive tosses of a fair coin, the simple events are S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT} with H = ‘head’ and T = ‘tail’ Another description of the possible outcomes of the coin tossing experiment is {‘three heads’, ‘two heals’, ‘one head’, ‘no heads’}. However, this is not a list of simple events since some of the outcomes, such as {‘two heads’}, can occur in several ways.