Mathematics can be applied to many daily life situations. In fact, math can be seen in nearly every aspect of life in some form or another. The trick of the matter is, is that most people are not aware of the fact that basic math skills can be used anytime and anywhere. For instance, the mathematical usage of probability can aid people in smart decision making, and can help people understand their odds. Statistically, probability refers to 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 (SOURCE). A rather obvious activity where probability applies is to is gambling. Casino games, such as Texas Hold Em’, can be played with an educated mind at hand. Knowing your odds of winning and the chances of winning money is valuable and should be available in peoples realm of knowledge. Similarly, Lotto 649 can be gambled on. If one has statistical probability enrichment at hand, however, then one can make quick intelligent choices and decisions. Probability 101 will educate, advise, and provide an insight into probability beneficiaries which can be applied to regular life situations, such as gambling, which will ultimately enrich one’s understanding of odds, and therefore, aid in making smart choices.

Chicago Manual Style (CMS):
probability. Dictionary.com. Dictionary.com Unabridged. Random House, Inc. http://dictionary.reference.com/browse/probability (accessed: March 30, 2011).

|Format |[reference #] Author(s), Book Title in Italics, edition (if available), Publisher, Place of publication, year | | |published. | |Highlighted example|[1] G. Chartrand and L. Lesniak, Graphs and Digraphs, 3rd ed., Chapman and Hall, Boca Raton, 2000. | |>2 authors |[#] T. W. Haynes, S. T. Hedetniemi, and P....

...Decision Analysis
Course Outline, Quarter I, 2006
Class Materials Topic
Hardcopy in Packet Other*
Introduction
1 Freemark Abbey Winery Structuring Decisions
Framework for Analyzing Risk
2 The North Star Concert North Star.xls Best Guess, Worst Case, Best Case; and Continuous Uncertainties
3 Engine Services, Inc.
Quick Start Guide to Crystal Ball
Analyzing Uncertainty, Probability Distributions, and Simulation Learning Module: Crystal Ball Litigate Demo
Engine Services.xls Language of Probability Distributions and Monte Carlo Simulation
4 Taurus Telecommunications Corporation: A New Prepaid Phone Card Learning Module: Tornado Sensitivity
Taurus Telecommunications.xls Sensitivity Analysis and Key Drivers
Time Value of Money
5 Dhahran Roads (A)
Evaluating Multiperiod Performance Multiperiod Pro Forma and NPV
6 Roadway Construction Company NPV, IRR, and Project Assumptions
Data and Distributions
7 Appshop, Inc. Simulating NPV
8 Lorex Pharmaceuticals
Introduction to Analytical Probability Distributions Lorex Exhibit 2.xls Distributions
9 Sprigg Lane (A) Sprigg2.xls Probability Distributions and Spreadsheet Modeling; Risk
10 The Waldorf Property
Chapter 11 of QBA: Text and Cases
Waldorf.xls Cumulative Distribution Functions, Adjustment for Risk
11 Amore Frozen Foods (A) Macaroni and Cheese Fill Targets
Sampling Amore.xls Sample Uncertainty
Regression
12 Hightower Department Stores:...

...Probability Theory and Game of Chance
Jingjing Xu
April 24, 2012
I. INTRODUCTION
Probability theory is the mathematical foundation of statistics, and it can be applied to many areas requiring large data analysis. Curiously, that the study on probability theory has its root in parlor games and gambling. In 17th century, dice gambling was a very common entertainment among the upper class. An Italian mathematician and gambler Gerolamo Cardano founded the concept of probability by studying the rules of rolling dice: since a die is a cube with each of its six faces showing a different number from 1 to 6, when it is rolled, the probability of seeing each number is equal. Therefore, some of the gamblers began to wonder, that taking a pair of dice and rolling them a couple of times, which has the larger probability of seeing a sum of 9 or seeing a sum of 10? What about seeing double sixes? In a correspondence between Blaise Pascal and Pierre Fermat, the problems were resolved, and this triggered the first theorem in the modern theory of probability.
II. BASIC DEFINITIONS
Definition 1
In probability theory, the sample space, often denoted Ω, of an experiment is the set of all possible outcomes....

...A Short History of Probability
Dr. Alan M. Polansky
Division of Statistics
Northern Illinois UniversityHistory of Probability 2
French Society in the 1650’s
! Gambling was popular
and fashionable
! Not restricted by law
! As the games became
more complicated and
the stakes became
larger there was a
need for mathematical
methods for computing
chances.History of Probability 3
Enter the Mathematicians
! A well-known gambler,
the chevalier De Mere
consulted Blaise Pascal
in Paris about a some
questions about some
games of chance.
! Pascal began to
correspond with his
friend Pierre Fermat
about these problems.History of Probability 4
Classical Probability
! The correspondence between Pascal and Fermat
is the origin of the mathematical study of
probability.
! The method they developed is now called the
classical approach to computing probabilities.
! The method: Suppose a game has
n equally
likely outcomes, of which
m outcomes
correspond to winning. Then the probability of
winning is m/n.History of Probability 5
Problems with the Classical Method
! The classical method requires a game
to be broken down into equally likely
outcomes.
! It is not always possible to do this.
! It is not always clear when possibilities are
equally likely.History of Probability 6
Experience
!...

...Hey guys, this is the probability Assignment. Last date for submission is 10 aug...
Q1. What is the probability of picking a card that was either red or black?
Q2. A problem in statistics is given to 5 students A, B, C, D, E. Their chances of solving it are ½,1/3,1/4,1/5,1/6. What is the probability that the problem will be solved?
Q3. A person is known to hit the target in 3 out of 4 shots whereas another person is known to hit the target in 2 out of 3 shots. Find the probability that the target being hit at all when they both try?
Q4. An investment consultant predicts that the odds against price of a certain stock will go up during the next week are 2:1 and the odds in the favor of the price remaining the same are 1:3.What is the probability that the price of the stock will go down during eth next week?
Q5. A bag contains 10 White and 6 Black balls. 4 balls are successfully drawn out and not replaced. What is the probability that they are alternately of different colors?
Q6.In a multiple-choice question there are 4 alternative answers, of which one or more are correct. A candidate will get marks in the question only if he ticks all the correct answers. The candidate decides to tick answers at random. If he is allowed up to 3 chances to answer the question, find the probability that he will get marks in the question?
Q7. A and B are two independent...

...Notation for the Binomial Distribution
P(S) The symbol for the probability of success
P(F) The symbol for the probability of failure
p The numerical probability of a success
q The numerical probability of a failure
P(S) = p and P(F) = 1 - p = q
n The number of trials
X The number of successes
The probability of a success in a binomial experiment can be computed with the following formula.
Binomial Probability Formula
In a binomial experiment, the probability of exactly X successes in n trials is
An explanation of why the formula works will be given in the following example.
Example 1:
A coin is tossed three times. Find the probability of getting exactly two heads.
Solution:
This problem can be solved by looking that the sample space. There are three ways to get two heads.
HHH, HHT, HTH, THH, TTH, THT, HTT, TTT
The answer is or 0.375.
The probability of a success in a binomial experiment can be computed with the following formula.
Binomial Probability Formula
In a binomial experiment, the probability of exactly X successes in n trials is
An explanation of why the formula works will be given in the following example.
Example 1:
A coin is tossed three...

...Hume on Probability
Hume begins section six of “An Enquiry Concerning Human Understanding” by stated right out that chance does not exist, but is merely a result of our ignorance of the causes behind any given event. He argues this by relating probability and belief. Belief arises when probability is at its most high. According to chance, any event may turn out anyway. Hume illustrates his point with a die. If a die were marked with one figure on four sides, while another figure on the other two sides, then it would be most probable that the die would land on the former side. If, however, the die had a thousand sides marked in one manner and only one side marked differently, then the probability of landing on the former mark would be higher. As such, our belief or expectation of this result would be higher1. As the chance of landing on one side of the die increases, the probability of that result also increases, and as such our belief in that result increases. As experience tells us that one result is more probable then another, so our mind construes the belief in that result. The nature of belief is thus constructed, as an experiment is repeated (such as the tossing of the fictional thousand sided die) and the result shows itself to be the same more often then not, then the idea of obtaining that result becomes more concrete and secure in the mind of the observer. Thus constituting a belief. There are...

...Conditional Probability
How to handle Dependent Events
Life is full of random events! You need to get a "feel" for them to be a smart and successful person.
Independent Events
Events can be "Independent", meaning each event is not affected by any other events.
Example: Tossing a coin.
Each toss of a coin is a perfect isolated thing.
What it did in the past will not affect the current toss.
The chance is simply 1-in-2, or 50%, just like ANY toss of the coin.
So each toss is an Independent Event.
Dependent Events
But events can also be "dependent" ... which means they can be affected by previous events ...
Example: Marbles in a Bag
2 blue and 3 red marbles are in a bag.
What are the chances of getting a blue marble?
The chance is 2 in 5
But after taking one out you change the chances!
So the next time:
* if you got a red marble before, then the chance of a blue marble next is 2 in 4
* if you got a blue marble before, then the chance of a blue marble next is 1 in 4
See how the chances change each time? Each event depends on what happened in the previous event, and is called dependent.
That is the kind of thing we will be looking at here.
"Replacement"
Note: if you had replaced the marbles in the bag each time, then the chances would not have changed and the events would be independent:
* With Replacement: the events are Independent (the chances don't change)
* Without Replacement: the events are Dependent (the chances...

...1) What is the value of understanding probabilities? Give specific examples of applications.
Your response to the question is due by Thursday, October 22nd.
Probability theorems tell us that, from the relative frequency of all possible events, a particular outcome will occur some computed percentage of the time.
Gambling on the slot machines takes into account the probability that after X amount of non matching pulls, there is a pull with a big pay out. There are people who sit at slot machines all day waiting for that pay out. There are other people that watch people at slot machines. The watchers wait until the machine is vacated and jump on in hope of cashing in on the probability that the next pull is a win.
To use probability in slot machines, you have to understand the average payout of the casino. When casinos advertise that their slot machines pay out an average of 90 percent, the fine print they don't want you to read says that you lose 10 cents from each dollar you put into the machines in the long term. (In probability terms, this advertisement means that your expected winnings are minus 10 cents on every dollar you spend every time the money goes through the machines.)
Suppose you start with $100 and bet a dollar at a time, for example. After inserting all $100 into the slot, 100 pulls later you'll end up on average with $90, because you lose 10 percent of your...