All the PROBABILITY content needed for MATHS CORE PAPER 1 (Grade 10-12).
By using these notes, you will be able to: Understand and work with dependent and independent events in addition to all the probability learnt in Grade 10 & 11, and use the fundamental counting principle to solve problems in...
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(AB) The probability of A or B occurring. is the symbol for or, it is also known
as union.
P (A and B) = P(AB) 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
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