Definition
The probability of an event E is given by:
for a large number of occurrences.
Probability of an Event not Occurring
The probability that an event A does not occur is given by:
Mutually Exclusive Events
Two events are mutually exclusive if they cannot occur simultaneously. The following Venn diagram represents two such events: A and B.
In this case the probability of event A or B occurring is given by:
The OR Rule
The above rule in works for events that are mutually exclusive. Events that are not mutually exclusive can occur simultaneously. In the following Venn diagram, the overlapping region, A∩B, represents two events occurring at the same time.
In this case, the probability of A or B (or both) occurring is given by:
Independent Events
If events A and B are independent than the probability of A occurring does not depend on B having occurred, and vice versa. For two independent events, the probability of both occurring is the product of the individual probabilities:
Conditional Probability
If two events are not independent, we can define the conditional probability, P(B|A), as the probability of B occurring, given that A has already occurred. The AND rule then becomes:
This rearranges to:
as an equation for conditional probability.
Tree Diagrams
These show the outcomes of a set of events and are useful for probability calculations. The probabilities are written on the branches of the tree. The diagram below is for two events, A and B.
Finally
The above notes are a revision summary rather than a tutorial. In order to understand probability fully, you should now look at some questions.