Download PROBABILITY – STUDY NOTES

P (E) =
PROBABILITY – STUDY NOTES
Number of favourable outcomes
----------------------------------Total number of outcomes
-
n(E)
n(S)
COMPLEMENTARY EVENTS
If P(E) is the probability of E occurring, then P(Ẽ) is the probability of E not occurring. Ẽ
is called the complementary event, and
P(E) + P(Ẽ) = 1.
P(Ẽ) = 1 - P(E)
EXPERIMENTAL PROBABILITY
The experimental probability of an event occurring is its relative frequency.
Relative frequency of an event =
Frequency of the event
------------------------Total frequency
THE MULTIPLICATION PRINCIPLE FOR COUNTING ARRANGEMENTS
1. If A can be arranged in m ways and B in n ways, then A and B together can be
arranged in m x n.
2. More generally, if A can be arranged in a ways, B can be arranged in b ways, C
can be arranged in c ways, etc., then A, B, C, … together can be arranged in a x b
x c … ways.
COUNTING ARRANGEMENTS
The number of ways in which n different items can be arranged is
n! = n (n - 1) x (n - 1) x … x 2 x 1
The number of ways in which n different items can be arranged in r positions is
n! = n (n - 1) x (n - 1) x …
[r terms]
Example - The number of ways 6 items can be arranged in 4 positions is
6x5x4x3
[4 terms]
COUNTING UNORDERED SELECTIONS
The number of unordered selections that can be made from n different items, when
there are r positions =
n x (n - 1) x (n - 2) x …
--------------------------r!
[r terms]
Example, the number of unordered selections that can be made from 6 different items,
when there are 4 positions =
6x5x4x3
-------------4x3x2x1
PROBABILITY TREE DIAGRAMS
 To calculate the probability of a particular outcome, multiply the probabilities
listed on the branches of each stage of the outcome.
 To calculate the probability of an event with two or more outcomes, add their
calculated probabilities together.
 For complementary events, P(‘at least one’) = 1 – P(‘none’)
EXPECTATION
If the probability of an event E is p and the experiment is conducted n times, the
expected number of times E will occur is n x p
Financial expectation is calculated by multiplying every possible financial outcome by
its probability and adding the results together.
Probability:
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Meaning of probability
Expectation
Ordered selections
Unordered selections
Tree diagrams
Probability in testing
Simulation
Multiplication