ENGRD 2700
Basic Axioms of Probability
1. The sample space of an experiment, denoted by
is the set of all possible outcomes
of that experiment. Note: the book uses cursive S.
2. An event is any collection of outcomes contained in a sample space
3. Union – element is in either A or B or both
AB
4. Intersection – element is on both A and B.
AB
a. Intersection is included in the union
b. If the intersection is the null set, A and B are disjoint (also called mutually exclusive)
5. Complement
A’ is the complement of A. It is the set of all elements in
that are not in A.
6. Probability
P1
P A P A P 1
hence
P A 1 P A
P A B P A P B P A B
Extend this to three events
P A B C P A P B P C P A B P A C P B C P A B C
7. Equally likely. See this in flips of a fair coin and rolls of a fair die
NA
PA N
Example. I roll a fair die. What is the probability I get either a one or a two?
