@@@ 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 ½ 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) È P*(R) = 1 P (R) Ç 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.