Chapter 4

Marginal Probability

Marginal probability is the probability of a single event occurring.

P(E) is likely to occur btwn...

0 and 1.

Relative Frequency Approach

A historic approach. this approach is one in which data is collected over a period of time. P(E)= Number of Times an event Occurred/ Total Number of Observations Ex: Defective radios, mortality tables, claims in the insurance industry. -Too few observations will not allow the historic method to work in an unbiased manner.

Experiment

A well-defined action, which leads to a single, well-defined outcome or result of an event.

Conditional Probability

Conditional probability is a ratio of joint probability divided by marginal probability. Reads from right to left!

Mutually Exclusive Events

Events are said to be mutually exclusive if the occurrence of one event precludes (shuts out or stops) the occurrence of another event

Subjective Approach

Here, probability is determined based on personal beliefs or expertise which is bolstered by some facts that will influence outcome. Often referred to as an educated-guess approach or best-guess approach. Used in business to make judgments about delivery dates to a customer or to a supplier performance or closing ratios for sales people as they make sales calls.

Complementary Events

If the failure of one event means the other must occur, the events are complementary. Complementary events exist when there are only two outcomes in the sample space. P(A)+P(A-bar)=1

Dependent Events

If the occurrence of an event depends on the occurrence of another event then the events are considered dependent.

Intersection

Intersecting probability is the set of ALL of the elements that are in both Set A and in Set B. A∩B -Often referred to as joint probability; joint probability of two events occurring simultaneously. The multiplication rule is useful in finding joint probability.

Classical Approach

Is a priori approach, meaning the probabilities can be determined before the fact. The classical approach is most often associated with games of chance or gambling. P(E)= Number of Ways the Event Can Occur/ Total Number of Possible Outcomes -The total number of possible outcomes is the sample space. This differs from the relative frequency approach in that the classical approach uses all possible outcomes where the relative frequency approach uses the total number of observations.

Joint Probability

Joint probability is the probability that two events will occur simultaneously.

Three Important Theorems

The Empirical Rule, Chebyshev's Rule, and the Central Limit Theorem.

Sample Space

The set of all possible outcomes (all events) for an experiment, also referred to as collectively exhaustive events.

Why Study Probability?

The theory behind probability provides a basis for evaluating the reliability of the conclusions reached and the inferences made about a data set.

Collectively-Exhaustive Events

To be collectively exhaustive, events must be all of the possible outcomes of an experiment. Sum of probabilities of collectively exhaustive events will equal one.

Independent Events

Two events are independent IF the occurrence of one event has NO effect on the probability that the second event will occur. -Rule: the data set must be finite (have predefined limits) and replacement must be done for events to be independent.

Union

Union is the set of ALL elements that are in A or B. A∪B. Use addition rule here!