Summary Probability Study Notes

Probability
MATHEMATICS GRADE 12
BY NIKITA VERMEULEN

, PROBABILITY
REVISION/BASICS

NOTATION

The probability of an event occurring will always lie between 0 and 1, where 0 is an impossible event and 1 is a
certain event.

 P(A)  The probability of event A occurring.
 P’(A)  The probability of event A not occurring (this is also called the compliment of A).
 P (A or B) = P(AB)  The probability of A or B occurring.  is the symbol for or, it is also known
as union.
 P (A and B) = P(AB)  The probability of A and B occurring.  is the symbol for and, it is also
known as intersection.
 P (A | B)  The probability of A occurring given that B has occurred.

MUTUALLY EXCLUSIVE EVENTS

If two events are mutually exclusive, it means that they cannot occur in the same trial.

For example (Mutually Exclusive Events):

If a trial is the tossing of a dice and event A is obtaining a 6 while event B is obtaining a 2, it is impossible too
obtain events A and B together.

For example (Not Mutually Exclusive Events):

If a trial is picking a card and event A is selecting a queen and event B is selecting a heart, it is possible to
obtain events A and B together.

For mutually exclusive events: P (A and B) = 0

THE ADDITION RULE

The addition rule states: P (A or B) = P(A) + P(B) – P (A and B)

If events A and B are mutually exclusive, then P (A and B) = 0 and the addition rule simplifies to:

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

COMPLEMENTARY EVENTS

If two events are complementary: P (not A) = P(A’) = 1 – P(A)

There are 2 conditions that have to be true for events to be complementary:

1. The events have to be mutually exclusive
2. P(A) + P(B) = 1



1