BUSS1020 Lecture Notes - Lecture 4: Collectively Exhaustive Events, Venn Diagram, Sample Space
5 Jun 2018
School
Department
Course
Professor
Understand basic probability concepts
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Learn about conditional probability
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Use Bayes theorem to revise probability
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Learn various counting rules
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LO:
Basic Probability Concepts
1.
Probability = the chance that a particular event will occur (always between 0 and 1)
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Impossible Event = an event that has no chance of occurring (probability = 0)
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Certain Event = an event that is sure to occur (probability = 1)
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Based on the ratio of the number of ways an event or outcome can occur to the
number of ways all outcomes can occur
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Can be expressed as a fraction: Favourable Outcomes/Possible Outcomes
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Used to analyse situations where each outcome is equally possible
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Examples: rolling a dice or flipping a coin
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Classical/A priori Probability
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Found by conducting trials or experiments e.g. in research studies
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Can be expressed as a fraction: Observed Favourable Outcomes/Total Observed
Outcomes
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Empirical Probability
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Based upon a person’s degree of confidence that an event will occur
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Used to make logically consistent decisions in the absence of better/more
objective information. The quality of these decisions will inevitably rely on the
accuracy of the subjective estimates.
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Subjective Probability
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Three Types of Probability
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An example of three approaches to assess the probability of an uncertain (discrete or
category) event:
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Assessing probability:
4. Basic Probability
Wednesday, 28 March 2018
8:44 AM
Textbooks Page 1
= each possible outcome of a variable
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Described by a single characteristics
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e.g. a customer purchases a product
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Simple event
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An event described by two or more characteristics
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e.g. customer purchases a product and pays more than $100
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Joint event
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All events that are not part of event A
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e.g. the customer does not purchase the product
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e.g. the customer pays $100 or more, or pays less than $100
Complement of an event A (denoted A')
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Events:
Textbooks Page 2
e.g. the customer pays $100 or more, or pays less than $100
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Collection of all possible events
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Sample space for tossing a coin consist of heads and tails
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Sample space
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Venn diagrams
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Contingency tables
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Decision trees
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Can show particular sample space
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Visualizing Events:
Textbooks Page 3
Document Summary
Probability = the chance that a particular event will occur (always between 0 and 1) Impossible event = an event that has no chance of occurring (probability = 0) Certain event = an event that is sure to occur (probability = 1) Based on the ratio of the number of ways an event or outcome can occur to the number of ways all outcomes can occur. Can be expressed as a fraction: favourable outcomes/possible outcomes. Used to analyse situations where each outcome is equally possible. Examples: rolling a dice or flipping a coin. Found by conducting trials or experiments e. g. in research studies. Can be expressed as a fraction: observed favourable outcomes/total observed. Based upon a person"s degree of confidence that an e(cid:448)ent (cid:449)ill occur. Used to make logically consistent decisions in the absence of better/more objective information. The quality of these decisions will inevitably rely on the accuracy of the subjective estimates.
