# 6.1 Basic Probability Concepts

## Probability: The relative possibility that an event will occur, as expressed by the ratio of the number of actual occurrences to the total number of possible occurrences.

It attempts to predict answers such as:
1. What are the chances of you rolling 7 or 11 in a row?
2. You may also be able to predict how likely something is to happen, for example: if the weather report forecast a 90% chance of rain, there is still a slight possibility that sunny skies will prevail. While there are no sure answers, in this case it probably will rain.

The Probability Scale
We can look at probability on a scale from 0 - 1.
0 - event never will occur
.5- the event and "not event" are likely to occur
1- always will occur
We are able to calculate probability in two different situations:
The first being Experimental. Experimental probability is when data is collected and the probabilities are calculated. For example, Xhovana and Nina are playing Tic Tac Toe, they play 10 games and it was observed that Nina won 7 out of the 10 games, so the probability of nina winning is 7 out of 10 or 70%.
The second situation of probability is Theoretical. Theoretical probability are when results are predicted using counting principles. For example, if Xhovana goes skiing and goes off a difficult jump 10 times you would expect half of the jumps for her to fall andGre the other half for her to land, so the probability of her to fall is 5 out of 10 or 50%.

### TERMS:

Statistical Fluctuation: If the number of repetitions is small, the two probabilites can be different.

Experiment: Probability problems involving repetition i.e. rolling a pair of die or flipping a coin

Trial: A step in a probability experiment in which an outcome is produced and tallied (each repetition is called a trial)

Event: Grouped outcomes with something in common

Probability of an Event A, P(A): A quantified measure od the likelihood that event A will occur. The probability of an event is always a value between 0 and 1

Sample Space (S): The set of all possible outcomes in a probability experiment
i.e. If Player A draws a 1 and Player B draws 2, you can label this outcome (1,2) in this particular game the result is the same for the outcomes (1,2) and (2,1) but with different rules it might be important who draws which number. So, it makes sense to view the two outcomes differently.

* Remember that the probability of P(A) is between 0 and 1
The probability of an event A, P(A) is:
P(A)= n(A)
n(S)
n(A)= # of ways event A can occur n(S)= total # of possible outcomes P(A')= probability of A not happening (compliment of A) P(A')= 1-P(A)

There are three basic types of probabilty, empirical, theoretical and subjective.
Empirical: The number of times that an event occurs in an experiment divided by the number of trials. The empirical probability is also known as the experimental or relative-frequency probability i.e if you had found that in the first ten trials, the product was greater than the sum four times, then the empirical probability of this event would be:
P(A)= 4
10
= 0.4
Theoretical: The probability of an event deduced from analysis of the possible outcomes. Theoretical probability is also called classical or a priori probability i.e What is the probability of flipping a coin 20 times and getting heads?
As we all know their are two sides to a coin (a head and a tail) we are expected to get heads 10 times if we flip the coin 20 times. This would be half or 50% probability. Since for each time we flip the coin once thier is 1/2 chance of getting heads.

Subjective: An estimate of the likelihood of an event based on intuition and experience (an educated guess) i.e estimate the probability that
a) the next pair of shoes you buy will be the same size as the last pair you bought
Solution: there is a small chance that the size of your feet has changed significantly or that different styles of shoes may fit you differently, so 80-90% would be a reasonable subjective probability that your next pair of shoes will be the same as your last pair.

The below PowerPoint Wiki contains examples that involve basic probability concepts

Started By Thread Subject Replies Last Post
Anonymous Hey 0 Nov 30 2009, 8:54 PM EST by Anonymous

Thread started: Nov 30 2009, 8:54 PM EST  Watch
Thank yu for posting this, it is very helpful :))
8  out of 10 found this valuable. Do you?
Keyword tags: (edit keyword tags)
Anonymous Mistakes 3 Feb 4 2008, 9:59 AM EST by Mr._D'Onofrio

Thread started: Nov 22 2007, 9:46 PM EST  Watch
there is so many mistakes in Powerpoint Presentation...........
14  out of 15 found this valuable. Do you?
Keyword tags: (edit keyword tags)
neelarjo Awesome Work! 0 Jun 6 2007, 1:10 AM EDT by neelarjo
Thread started: Jun 6 2007, 1:10 AM EDT  Watch
I'm supposed to constructively criticize here...but I really can't find any mistake because the concept has been explained very very well.....but I would like to say that the examples posted are really easy...(yea I maybe good but its just childs-play solving them)...but showing a few challenging questions would explain the concept in far greater detail..... (maybe a lot if possible since all this contains is reading material and people like me are not really those reading types....maybe if u showed it using examples, it could get into the head easily LOL......adding a few homework questions could enhance this topic as well.....otherwise, its really done well...
4  out of 4 found this valuable. Do you?
Keyword tags: None (edit keyword tags)

 Subject: Message: Category: General Discussion
 6.1 Basic Probability Concept.ppt (Powerpoint Presentation - 888k) posted by inhee   May 18 2007, 9:37 PM EDT Power point presentation

#### Related Content

(what's this?Related ContentThanks to keyword tags, links to related pages and threads are added to the bottom of your pages. Up to 15 links are shown, determined by matching tags and by how recently the content was updated; keeping the most current at the top. Share your feedback on Wetpaint Central.)
 .... PCI students Park City Independent Hi! Hello math its easy O.o alia Hey 7.2 Binomial Distributions 6.5 Mutually Exclusive Events