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Title: 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
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