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Welcome to Chapter 5 MBA 541

BENEDICTINE UNIVERSITY

• Probability - Distributions

• A Survey of Probability Concepts

• Chapter 5

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Chapter 5

Please, Read Pages 139 – 146

in Chapter 5 in Lind before viewing this presentation.

Only part of Chapter 5 will be covered.

StatisticalTechniques in

Business &Economics

Lind

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Goals

When you have completed this chapter, you will be able to:

• ONE– Define Probability.

• TWO– Describe the classical, empirical, and

subjective approaches to probability.

• THREE– Understand the terms: experiment, event, and

outcome.

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What is a Probability?

A Probability is a measure of the likelihood that an event in the future

will happen.

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Definitions of Probability

• There are three definitions of probability: classical, empirical, and subjective.

• The Classical definition applies when there are n equally likely outcomes.

• The Empirical definition applies when the number of times the event happens is divided by the number of observations.

• Subjective probability is based on whatever information is available.

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Definition of Experiment

An Experiment is the observation of some

activity or the act of taking some measurements

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Definitions of Outcome and Event

• An Outcome is the particular result of an experiment.

• An Event is the collection of one or more outcomes of an experiment.

• The following items illustrate these definitions:

– Experiment: A fair die is cast.

– Possible Outcomes: the numbers 1, 2, 3, 4, 5, 6

– One Possible Event: The occurrence of an even number. That is, the collection of the outcomes 2, 4, and 6.

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Mutually Exclusive Events

• Events are Mutually Exclusive if the occurrence of any one event means that none of the others can occur at the same time.

• As an example of Mutually Exclusive:– Rolling a 2 precludes rolling a 1, 3, 4, 5, 6 on

the same roll.

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Collectively Exhaustive Events

• Events are Collectively Exhaustive if at least one of the events must occur when an experiment is conducted.

• As an example of Collectively Exhaustive:– Consider a die-tossing experiment.– One possible event is rolling an even number.– Another possible event is rolling an odd number.– These two events are Collectively Exhaustive because

every outcome of a die-toss will be either even or odd.

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Classical Probability

• Classical Probability is based on the assumption that the outcomes of an experiment are equally likely.

• The value for the Classical Probability will always be between 0 and 1 inclusive and is given by the following formula:

Number Of Favorable OutcomesProbability =

Total Number Of Possible Outcomes

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Example 1

• This is an example of the classical definition of probability.

• What is the probability of drawing the Queen of Hearts from an honest deck of cards?

1P A = = 0.0192

52

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Empirical Probability

• With Empirical Probability, the probability of an event happening is determined by observing what fraction of the time similar events happened in the past.

• The value for the Empirical Probability will always be between 0 and 1 inclusive and is given by the following formula:

Number Of Times Event Occured in PastProbability =

Total Number Of Observations

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Example 2

• This is an example of the empirical definition of probability.

• Throughout her teaching career Professor Jones has awarded 186 A’s out of 1,200 students.

• What is the probability that a student in her section this semester will receive an A?

186P A = = 0.155

1200

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Subjective Probability

• Subjective Probability is used when there is little or no past experience or information on which to compute a probability.

• Examples of subjective probability are:

• Estimating the probability that the Washington Redskins will win the Super Bowl this year.

• Estimating the probability that mortgage rates for home loans will top 8 percent.

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Summary of Approaches to Probability

Classical Probability

EmpiricalProbability

Objective Subjective

Approaches to Probability

Based on available information

Based on equally likely outcomes

Based on relative

frequencies

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Summary and Conclusions

• Introduced the language of probability.

• Outlined and introduced the concepts of probability.

• Probability theory helps to quantify the probability (or risk) of future events.

• Probability theory can help with decision making via risk analysis.