1 A Simple Introduction to Probability By Luke Fenton-Glynn 1. Unconditional Probability Here is the ‘universe’, the space of all possibilities … Figure 1. ‘Events’ are represented by areas within this space … Figure 2. A and B here are two non-mutually exclusive events. E.g. A = the event of it snowing in London on Christmas Day. B = the event of a Democrat winning the next US presidential election. A and B are not mutually exclusive. Hence there is some ‘overlap’ between the events. The area of overlap (which is the shaded area in the diagram) represents the possibility that A and B both occur (that it snows in London on Christmas Day and a Democrat wins the next US presidential election). In probability theory (and set theory), A ∩ B is often used to denote the occurrence of both A and B (A & B or A ∧ B or A.B are other notations sometimes used for the same thing). The term ‘event’ is used quite loosely in probability theory and set theory: any region of the space of possibilities counts as an ‘event’. So the region A ∩ B is an event: the event of it snowing in London on Christmas Day and a Democrat winning the next US presidential election. B A∩B A