@@@ A Simple Overview of Probability & Odds @@@

 

Definition: Probability is concerned with events of chance or uncertainity. ( Click on Probability! )

Probabilities are normally and usually represented as fractions e.g. 2/3 or 4/5

 

Scale of Probability: Impossible Maybe Certain

|-------------------------|-----------------------|

0 Low High 1

 

Sample Space (Universe of Event)

 

A listing or diagram of all possible outcomes from an experiment or occurrence.

 

Specific Event (Subset of Universe)

 

Simple (single event) or Non-Simple (multiple events) of chance.

 

Types of Probabilities for an Experiment (Event) of Chance or Uncertainity.

P = Probability * = Not P* = Not Probability

 

 

Probability Experiment: Draw a Marble

from a box containing ( 9 ) marbles.

 

 

Marbles: Blue Blue Blue Blue

Red Red Red Green Green

 

 

@@@ Probability of Success = (Success / Total ) Probability of Failure* = ( Failure / Total )* @@@

 

 

 

P (R) = 3/9

 

 

P (G) = 2/9

 

 

P (B) = 4/9

 

 

P* (R) = 6/9

 

 

P* (G) = 5/9

 

 

P* (B) = 3/9

 

 

P (R) P*(R) = 1 P (R) P*(R) = 0

 

 

 

The Sum of P and P* equals 1. The intersection of P and P* equals 0.

 

 

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Definition: Odds represents the probability of an event occurring and/or happening. ( Click on Odds! )

 

Odds are normally and usually represented as ratios e.g. 2:3 or 2 to 3

 

 

 

Summary of Odds: Marble Experiment

Drawing marble from box (9) marbles.

 

 

Marbles: Blue Blue Blue Blue

Red Red Red Green Green

 

 

 

Simple Example of the Odds for the above Experiment of Chance or Uncertainity.

Odds equals ratio of Probabilities. Thus represent Odds then reduce as ratios.

 

 

Odds in favor of Red event: Of (R) = 3/9 : 6/9 = 3 : 6 or 3 to 6

 

Odds against Red event: Oa (R) = 6/9 : 3/9 = 6 : 3 or 6 to 3

 

 

Odds in favor of Blue event: Of (B) = 4/9 : 5/9 = 4 : 5 or 4 to 5

 

Odds against Blue event: Oa (B) = 6/9 : 3/9 = 6 : 3 or 6 to 3

 

 

Odds in favor of Green event: Of (G) = 3/9 : 6/9 = 3 : 6 or 3 to 6

 

Odds against Green event: Oa (G) = 6/9 : 3/9 = 6 : 3 or 6 to 3

 

 

Thus using Probabilities to develop Odds readily shows that it is more likely to not get a RED.

 

Tom Love Malone College Fall 2003

 

Reference for this information on P & O: Fundamentals of Mathematics by Edwin I. Stein