H2: Sample Space, Relationships Among Events and Rules of Probability

Probability

What is used to describe the phenomenon of chance or randomness of events to occur?

guarantees, likelihood

Probability does not deal with […], but with the […] of an occurrence of an event.

subjective, theoretical or classical probability

Probabilities sometimes are […] (aka […] or […]); and is based on past experience and judgment of the person to determine whether a specific outcome is likely to occur.

Subjective Probability

It contains no formal calculations and differ from person to person, and they contain a high degree of personal bias.

1. Opinion Polls

2. Experience and Judgment

3. Delphi Method

What are several methods for making subjective probability assessments?

Opinion Polls

What can be used to help determining subjective probabilities for possible election returns and potential political candidates?

‘Experience’ and Judgment

What relate back to upbringing as well as other events the person has witnessed throughout his life?

Experience and ‘Judgment’

Example: A production manager, for instance, might believe that the probability of manufacturing a new product without a single defect is 0.85.

Delphi Method

In what method a panel of experts is assembled to make their predictions of the future?

objectively, empirical or experimental probability

Probabilities are […] (aka […] or […]) based on examining past data and using logical and mathematical equations involving the data to determine the likelihood of an independent event occurring.

P(E) = n(E) / n(S)

What is the Probability Formula?

P(E) or Experiments

In Probability Formula: P(E) = n(E) / n(S) ;

Which refers to situation involving chance or probability that produces an event?

n(S) or Sample Space

In Probability Formula: P(E) = n(E) / n(S) ;

Which refers to set of all possible outcomes of an experiment, that is, any subset of the sample space?

n(E) or Event

In Probability Formula: P(E) = n(E) / n(S) ;

Which refers to one or more of the possible outcomes of a single trial of an experiment?

1. 0 ≤ P(E) ≥ 1

2. P(∅) = 0

3. P(S) = 1

What are the basic properties of probabilities?

Property 1: 0 ≤ P(E) ≥ 1

What basic property of probability refers to: the probability, P, of any event or state of nature occurring lies between greater than or equal to 0 or 0% and less than or equal to 1 or 100%?

Property 2: P(∅) = 0

What basic property of probability refers to: the probability of an event will not be lass than 0 because it is not possible (impossible) or can never occur?

Property 3: P(S) = 1

What basic property of probability refers to: the probability of an event will not be more than 1 because 1 is certain that something will happen (sure event)?

OR

What are the events involving in the addition rule of probabilities?

AND

What are the events involving in the multiplication rule of probabilities?

1. Mutually Exclusive (Special Addition Rule)

2. Not Mutually Exclusive (General Addition Rule)

What are the addition rule of probabilities?

Mutually Exclusive (Special Addition Rule)

This is wherein the probability that A or B will occur is the sum of the probability of each event.

Not Mutually Exclusive (General Addition Rule)

This is wherein the probability that A or B will occur is the sum of the probabilities of the two events minus the probability that both will occur.

1. Independent Event (Special Multiplication Rule)

2. Dependent Event (General Multiplication Rule)

What are the multiplication rule of probabilities?

Independent Event (Special Multiplication Rule)

This is wherein if the occurrence or nonoccurrence of one of the events does not affect the likelihood that the other event will occur.

Dependent Event (General Multiplication Rule)

This is wherein if the occurrence of one event does affect the likelihood that the other event will occur.

Multiplication Rule

What is the fundamental principle of counting is often referred to?

independent

The multiplication principle of counting only works when all choices are […] of each other.

Permutation

What is a counting technique which refers to the arrangement (or ordering) of a set of objects, from first to last, where the order in which the objects are selected does matter?

Combination

What is a selection of objects from a collection in any order as oppose to permutations which deal with the ordered arrangements of objects?