# Probabilty and Set Notation

- Created by: thereviser
- Created on: 19-12-11 21:48

Probability and Set Notations

Revision Notes from www.s-cool.co.uk

See the website for more topics.

#### Probability

The probability that an event, **A**, will happen is written as **P(A)**.

The probability that the event **A**, does not happen is called the **complement of A** and is written as **A'**

As either **A** must or must not happen then,

**P(A') = 1 - P(A)** as probability of a certainty is equal to 1.

#### Set notation

**If A and B are two events then:**

**A B** represents the event 'both A and B occur'

**A B** represents the event 'either A or B occur'

#### Mutually Exclusive Events

Two events are mutually exclusive if the event of one happening excludes the other from happening. In other words, they both cannot happen simultaneously.

**For exclusive events A and B then:**

**P(A or B) = P(A) + P(B) this can be written in set notation as**

**P(A B) = P(A) + P(B)**

This can be extended for three or more exclusive events

P(A or B or C) = P(A) + P(B) + P(C)

*Handy hint:* Exclusive events will involve the words 'or…

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