STA 2023
Basic Concepts of Probability
and Counting
Probability Experiments
 A probability
experiment is an action, or trial, through
which specific results are obtained.
 The
result of a single trial is an outcome.
 The
set of all possible outcomes of a probability
experiment is the sample space.
 An
event is a subset of the sample space which may
have more than one outcome.
 Example
1: Identify the sample space of the
probability experiment and determine the number of
outcomes in the sample space.
 Tossing three Coins.
Start
H
T
H
T
H
T
H
T
H
T
H
T
H
T
HHH
HHT
HTH
HTT
THH
THT
TTH
TTT
 Sample
space:
{HHH,HHT,HTH,HTT,THH,THT,TTH,TTT}
 Number of Outcomes: 8
Simple Event
 A simple
event is an event that consist of a single
outcome.
 Example
2: For each event, determine the
number of outcomes and state whether the
event is simple or not.

Rolling an even number on a six-sided die.
3

outcomes, not a simple event
Pulling the Queen of Hearts out of a standard deck
of playing cards.
 1outcome,
simple event.
The Fundamental
Counting Principle

 Example
3: A shirt company has 4 designs each of
which can be made with short or long sleeves. There
are 7 color patterns available. How many different
shirts are available from this company?

56 shirts
 Example
4: How many license plates can be made
consisting of 2 letters followed by 3 digits?

676,000 license plates
Types of Probability

 Example

5: Identify the type of probability being used
The probability that a train will be in an accident on a
specific route is 1%
 Empirical

The probability that interest rates will rise during the
summer is 0.05.
 Subjective

The probability of winning California's Pick Three lottery
is 1/1000.
 Classical
Other Properties
 Law

of Large Numbers
As an experiment is repeated over and over, the
empirical probability of an event approaches the
theoretical probability of the event
 Range

of Probabilities
The probability of an event E is between 0 and 1,
inclusive.
 Complements


The complement of event E is the set of all outcomes in
a sample space that are not included in event E.
Denoted as E’ (e prime)