Probabilty and Set Notation

Probability and Set Notations

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

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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…