@@@ 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: Tossing a Die onto a table or the floor. |
Since a Die is a Cube with 6 faces: 1, 2,
3, 4, 5,
6 |
@@@ Probability of Success = (Success / Total ) Probability of Failure* = ( Failure / Total )* @@@
|
P (2) = 1/6 |
P (Odd) = 3/6 |
P (N<5) = 4/6
|
|
P* (2) = 5/6 |
P* (Odd) = 3/6 |
P* (N<5) = 2/6 |
|
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: Die Experiment Tossing a Die with 6 faces onto floor. |
Since a Die is a Cube with 6 faces: 1, 2,
3, 4, 5,
6 |
Simple Example of the Odds for the above Experiment
of Chance or Uncertainity.
Odds represent a ratio of Probabilities. Thus represent Odds then reduce as ratios.
Odds in favor of Two event: Of (N=2) = 1/6 :
5/6 = 1 : 5 or 1 to 5
Odds against Two
event: Oa (N=2) = 5/6 :
1/6 = 5 : 1 or 5 to 1
Odds in favor of Odd event: Of (N is Odd) = 3/6 :
3/6 = 3 : 3 or 3 to 3
Odds against Odd event: Oa (N is Odd) = 3/6 :
3/6 =
3 : 3 or 3 to 3
Odds in favor of N<5 event: Of (N<5) = 4/6 :
2/6 = 4 : 2 or 4 to 2
Odds against N<5
event: Oa (N<5) = 2/6 :
4/6 = 2 : 4 or 2 to 4
Thus using Probabilities
to develop Odds readily shows that it is more likely to not
get a Two.
Tom Love Malone College Fall 2003