Probability Concepts

1
Probability Concepts
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
2
Events and Probability

• An activity for which the outcome is uncertain is
  an experiment.
• An event consists of one more possible outcomes
  of the experiment.

Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
3
Relative Frequency Approach
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
4
Datacomp Survey
M a male is selected F a female is
selected U the person selected is under 30 B
the person selected is between 30 and 45 O
the person selected is over 45
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
5
Marginal Probability
Marginal Probability the probability of a single
event used to define the contingency table. P(M)
120/200 .6 P(F) 80/200 .4 P(U)
.5 P(B) .25 P(O) .25
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
6
Complement of an Event

• The Complement of an event A is the event that A
  does not occur. ?
• P(A) P(?) 1
• P(M) 1 - P(M) .4

Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
7
Joint Probability

• The probability of the occurrence of two events
  at the same time.
• The probability of selecting a person who is a
  female and under 30
• P(F and U) 40/200 .2

Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
8
Union of Events

• The Union of events is the probability of either
  event A or event B occurring.
• The probability of selecting a person who is
  Male or under 30.
• P(M or U) (120 40) / 200 .8

Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
9
Conditional Probability

• Whenever you are given information and are asked
  to find a probability based on this information,
  the result is a Conditional probability.
• P(AB)

Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
10
Independent Events

• If the P(A) P(AB) then event A is said to be
  independent of event B.
• P(M) P(MU) .6
• Thus event M is independent of event U.

Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
11
Mutually Exclusive Events

• If an event can not occur when another event has
  occurred the two events are said to be Mutually
  Exclusive.
• Selecting a Male and a Female are mutually
  exclusive events.
• P(MF) 0

Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
12
Additive Probability Rules

• General Additive Rule
• P(A or B) P(A) P(B) - P(A and B)
• Special Additive Rule
• If A and B are mutually exclusive then
• P(A or B) P(A) P(B)

Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
13
Conditional Probability Rules

• General Conditional Probability Rule
• P(AB) P(A and B) P(B) ? 0
• P(B)
• Special Conditional Probability Rule
• If A and B are independent then
• P(AB) P(A) P(A and B) P(A) ?P(B)

Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
14
Tree Diagrams

• The probability of the event on the right side
  (say, event B) of the tree is equal to the sum of
  the paths that is, all probabilities along a
  path leading to event B are multiplied, and then
  summed over all paths leading to B.

Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
15
Figure 4.11
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
16
Counting Rules

• Counting Rules determine the number of outcomes
  that exist for a certain broad range of
  experiments.
• Filling Slots
• Permutations
• Combinations

Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
17
Filling Slots

• Use counting rule 1 to fill k different slots.
  Let
• n1 the number of ways to filling the first slot
• n2 the number of ways to filling the second
  slot after the first slot is filled
• ?
• nk the number of ways to filling the kth slot
  after slots 1 though k - 1
• The number of ways of filling all k slots is
• n1 ? n2 ? n3 ? ? nk

Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
18
Permutations

• Permutations is the counting situation in which
  you select people without replacement and where
  order of selection is important.

Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
19
Combinations

• Combinations is the counting situation in which
  you select people without replacement and where
  order of selection is not important.

Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing