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Welcome to Chapter 5 MBA 541

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BENEDICTINEUNIVERSITY

- Probability - Distributions
- A Survey of Probability Concepts
- Chapter 5

Please,

Read Pages 139 – 146 in Chapter 5 in Lind before viewing this presentation.

Only part of Chapter 5 will be covered.

Statistical

Techniques in

Business &

Economics

Lind

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.

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

- There are three definitions of probability: classical, empirical, and subjective.
- The Classical definition applies when there are n equally likely outcomes.
- The Empiricaldefinition 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.

An Experiment is the observation of some activity or the act of taking some measurements

- 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.

- 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.

- 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.

- 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:

- 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?

- 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:

- 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?

- 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.

Approaches to

Probability

Subjective

Objective

Classical

Probability

Empirical

Probability

Based on available information

Based on equally likely outcomes

Based on relative frequencies

- 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.