Probability and Set Notations
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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.
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…