## 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.