Statistics for Managers 5th Edition

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Statistics for Managers 5th Edition

• Chapter 4
• Basic Probability

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Chapter Topics

• Basic probability concepts
• Sample spaces and events, simple probability,
  joint probability
• Conditional probability
• Statistical independence, marginal probability
• Bayess Theorem

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Terminology

• Experiment- Process of Observation
• Outcome-Result of an Experiment
• Sample Space- All Possible Outcomes of a Given
  Experiment
• Event- A Subset of a Sample Space

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Sample Spaces

• Collection of all possible outcomes
• e.g. All six faces of a die
• e.g. All 52 cards in a deck

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Events

• Simple event
• Outcome from a sample space with one
  characteristic
• e.g. A red card from a deck of cards
• Joint event
• Involves two outcomes simultaneously
• e.g. An ace that is also red from a deck of
  cards

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Visualizing Events

• Contingency Tables
• Tree Diagrams

Ace Not Ace
Total
Black 2 24 26
Red 2 24 26

Total 4 48 52

Ace
Red Cards
Not an Ace
Full Deck of Cards
Ace
Black Cards
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Not an Ace
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Special Events
Null Event

• Impossible event
• e.g. Club diamond on one card draw
• Complement of event
• For event A, all events not in A
• Denoted as A
• e.g. A queen of diamonds A all cards
  in a deck that are not
  queen of diamonds

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Contingency Table
A Deck of 52 Cards
Red Ace
Not an Ace
Total
Ace
Red
2
24
26
Black
2
24
26
Total
4
48
52
Sample Space
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Tree Diagram
Event Possibilities
Ace
Red Cards
Not an Ace
Full Deck of Cards
Ace
Black Cards
Not an Ace
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Probability
Certain
1

• Probability is the numerical measure of the
  likelihood that an event will occur
• Value is between 0 and 1
• Sum of the probabilities of all mutually
  exclusive and collective exhaustive events is 1

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Impossible
0
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Types of Probability

• Classical (a priori) Probability

P (Jack) 4/52

• Empirical (Relative Frequency) Probability

Probability it will rain today 60

• Subjective Probability

Probability that new product will be successful
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Computing Probabilities

• The probability of an event E
• Each of the outcomes in the sample space is
  equally likely to occur

e.g. P( ) 2/36
(There are 2 ways to get one 6 and the other 4)
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Probability Rules

• 1 0 P(E) 1
• Probability of any event must be between 0
  and1
• 2 P(S) 1 P(?) 0
• Probability that an event in the sample space
  will occur is 1 the probability that an event
  that is not in the sample space will occur is 0
• 3 P (E) 1 P(E)
• Probability that event E will not occur is 1
  minus the probability that it will occur

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Rules of Addition

• Special Rule of Addition
• P (AuB) P(A) P(B) if and only if A and B are
  mutually exclusive events
• General Rule of Addition
• P (AuB) P(A) P(B) P(AnB)

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Rules Of Multiplication

• Special Rule of Multiplication
• P (AnB) P(A) x P(B) if and only if A and B are
  statistically independent events
• General Rule of Multiplication
• P (AnB) P(A) x P(B/A)

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Conditional Probability Rule

• Conditional Probability Rule
• P(B/A) P (AnB)/ P(A)
• This is a rewrite of the formula for the general
  rule of multiplication.

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Bayes Theorem
What is the probability that Bill filled a
prescription that contained a mistake?
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Bayess Theorem
Adding up the parts of A in all the Bs
Same Event
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Bayes Theorem (cont.)
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Bayes Theorem (cont.)
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Chapter Summary

• Discussed basic probability concepts
• Sample spaces and events, simple probability, and
  joint probability
• Defined conditional probability
• Statistical independence, marginal probability
• Discussed Bayess theorem

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