Basic Statistics
Quarter 3- Module 1:
Properties of a Probability
Function
8
Part I. Introduction and Discussions
We learned from quarter 2 that we could form new events by
applying the set operations of union, intersection, complement, or
combinations of these operations on other events. We also discussed
the special interpretations of these events. Let us review: (i) A ∪ B=
event that at least one of A or B will occur; (ii) A ∩ B= event that both
A and B will occur; and (iii) Ac= event that A will not occur.
It is important to learn how to express events as a composition of
other events in order to compute for probabilities using the properties
of the probability function. So far, the only properties of the probability
function that we know are the properties stated in Kolmogorov’s
definition of probability.
We now state three additional properties as theorems 3.1.1 to 3.1.3.
we can derive all these properties using Kolmogorov’s definition. The
focus of this module is to illustrate how we can use the formulas stated
in these theorems to compute for the probabilities of events that that
are expressed as a composition of other events.
Theorem 3.1.1
If A is an event then P(Ac)= 1− P(A).
Theorem 3.1.2
If A and B are events then P(A ∩ Bc)= P(A) − P(A ∩ B).
Theorem 3.1.3
If A and B are events then P(A ∪ B)= P(A)+P(B) − P(A ∩ B).
