Probabilty and Set Notation

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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 (http://www.s-cool.co.uk/a-level/assets/revise_its/alevel/maths/probability/image012.gif) B represents the event 'both A and B occur'

A (http://www.s-cool.co.uk/a-level/assets/revise_its/alevel/maths/probability/image014.gif) 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 (http://www.s-cool.co.uk/a-level/assets/revise_its/alevel/maths/probability/image014.gif) 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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