Download 6. Introduction to Probability

Introduction to Probability
BUSA 2100, Sections 4.0, 4.1, 4.2
Need For and Uses Of
Probability
Probabilities are necessary because we
live in an uncertain world. Probabilities
are a way of quantifying uncertainty.
 Definition: A probability is a numerical
measure of the likelihood or chance that
an event will occur.
 Probability was first used in the context
of gambling, i.e. cards, coins, and dice.

More Uses of Probability
Cards, coins, and dice still provide good
examples for explaining probabilities.
 Other uses of probability include: weather forecasting, biology, political science, insurance, investments, & sales.
 Life and car insurance rates are based
upon life expectancies and probabilities
of auto accidents.

Events and Probabilities
Definition: An event is one or more of
the possible outcomes of an activity,
e.g. “even number on a die”.
 Notation: P(E) represents the probability
that event E will occur.”
 The probability of an event is always
between 0 and 1. (fraction or decimal)

Types of Events
Def.: The complement of an event E,
denoted by EC, is the opposite of event E.
 Example: If E = “will rain today”, then EC =
“will not rain today.” Formula for EC?


Definition: Two or more events are
mutually exclusive if only one of them
can occur at a time.
Types of Events, Page 2
Example 1: F = “car made by Ford
Motor Co.”, G = “car made by General
Motors” are mutually exclusive events.
 Example 2: D = “person who has a
daughter”, “S = “person who has a sister” are not mutually exclusive events.
 Definition: A set of events is exhaustive
if it includes all possible outcomes.

Types of Events, Page 3
Example 1: For primary colors,
R = “red”, B = “blue”, Y = “yellow” are
exhaustive events.
 Example 2: S = “sophomore”,
J = “junior” are not exhaustive events.
 If a set of events is mutually exclusive
and exhaustive, the probabilities of
these events must sum to 1.

Types of Events, Page 4
Definition: Two or more events are
equally likely if each event has the
same probability of occurrence.
 Examples: A 1, 2, 3, or 4 on a die;
a boy or girl baby.

Ways to Obtain Probabilities
First method: The classical formula,
P(E) = (number of outcomes pertaining
to event E) / (total number of possible
outcomes).
 The classical formula is true only if the
outcomes are mutually exclusive,
exhaustive, and equally likely.

Obtaining Probabilities, p. 2

Example 1: If 2 dice are rolled, what is
the probability that the sum of the
numbers on the dice will be 8?
Obtaining Probabilities, p. 3


Example 2: In a family of 3 children,
what is the probability of 2 boys &1 girl?
Obtaining Probabilities, p. 4
Advantage: Classical formula has nearly
perfect accuracy.
 Disadvantage: Often a list or count of all
possible outcomes is not practical.

Obtaining Probabilities, p. 5
Second method: The relative frequency method -- using relative
frequencies of past occurrences as
probabilities for the present and future.
 Advantages: Method usually has very
good accuracy, is easy to use, and is
applicable to a wide variety of
situations.

Obtaining Probabilities, p. 6
Example. Past daily TV sales for a firm:
Daily Sales No. of Days

(Frequencies)

50
9

55
18

60
36

65
27

Obtaining Probabilities, p. 7


Third method: Subjective method -- a
probability based on relevant information,
experience, judgment, and intuition, but not
based on a specific formula.
It is an informed estimate.
Obtaining Probabilities, p. 8

Example 1: What is the probability that
the inflation rate will be less than 4%
next year?
Obtaining Probabilities, p. 9

Example 2: What is the probability that the
Braves will the NL championship?

The subjective method is the least accurate
method of obtaining probabilities.
But subjective probabilities are better than
none at all.
