“Odds are Against your Breaking that Law of Averages” In this article James Trefil discusses key issues concerning the use of statistics and the study of probability. He gives us historical background on the development of probability studies tied to games of chance; basic ideas of probability that are part of our mental arsenal and can be used in all kinds of unexpected situations; implications on statistics. First of all, he talks about that probabilities take their place in every part of our life, how can we put statistics in our life, how can we calculate the probability, which is born in the study of games of chances. There is a calculation of rolling a die without getting a double “6” and he says that conventional thinking reveals that breakeven point in rolling a die for four times gives us 24 but it is revealed by De Mere that it is not 24 it is 25 for the double die game. And then he says that throwing die without getting 6 is 5/6 and if it would be thrown for four times iut gives us 5/6 times 4 equals .48 that means that we have 0.48 percent to win the game. Another example is roulette game, he says that in roulette there are 18 black 18 red slots in conventional way we night think that we have chance of 18/36 which is 50% of winning but there is also extras such as 0 and 00 numbers so we have 38 numbers and we have the chance of 18/38=47 percent. It is said in the article that there are two central ideas of probability; first is we divide number of ways that we can be successful by the number of ways that things can turn out as in the example of rolling a die. The second one is that the probability of an independent event doesn’t depend on what happened in the past. For example what comes when heads or tails when you throw the coin doesn’t depend on the last one. But if you try picking a card from a deck of cards it is depended if you take out each card from the deck when you pick them. Risk is defined...

...it was necessary to establish the probability of occurrence, the impact it will have on the project and the cost of mitigation. This was also necessary in ensuring that the project team is not distracted by symptoms but rather, root causes.
2.2 Risk Analysis Procedure
The risk analysis was preceded by a risk identification phase that involved all members of the team. The object was to identify all the related risks that could possible hinder the execution of the project. The risks identified were grouped into five (5); Force Majeure (as a result of torrential rain), Theft of materials, Accidental errors (lack of knowledge on safety), Power Losses (due to electrical power failure or disruption, Human errors (due to limited skills and expertise). All of the risks were assessed as negative.
The qualitative risk analysis was started with a Probability/Impact assessment. Depending on the perceived gravity of the risks being considered, low, medium and high were assigned.
Table 2a) Probability & Impact Assessment
Identified Risk Events Risk Probability Risk Impact
1. Force Majeure Medium High
2. Theft of Materials Low Low
3. Accidental Errors Low Medium
4. Power Losses Medium Low
5. Human Errors Medium Medium
Of the five risks identified, the risk of force majeure was considered the most significant, attracting a medium probability and a high impact. The next stage was to assign values of 1-5...

...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:...

...Significance of the study
This study aims to propose an intervention program covering the secondary mathematics subject. The academe, both faculty and students, shall benefit through having a guided program to increase the quality of the mathematics teaching-learning process. administrators and the university itself will also benefit once the proposal had been approved, executed and positively assessed, producing competent students, thus encouraging more patrons who seek for quality education. This study may also be a basis and reference for future researches and researches .The new curricula are organized in three strands of objectives: knowledge, abilities and attitudes/values. According to those we interviewed at the Ministry, one of the major aims was definitively the improvement of the attitudes of the students towards mathematics. The new curricula suggested a more intuitive approach to the mathematical concepts, with emphasis in graphical representations and real world situations. Other new features included the introduction of probability and statistics from an earlier grade level and a greater attention to geometry. In terms of teaching methodologies, the use of calculators was recommended from grade 7 on and some attention was given to active methodologies and group work.The new discipline of quantitative methods was ment for students of humanistic areas who did not have formerly mathematics in...

...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...

...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...

...two chance events mentioned above, there is another chance event concerning whether the market research predicts that the zoning change will be approved. The consequence is that the company will have different profits or losses.
Data analysis:
Below is a timeline showing the sequence of events taking place from now to November where the results of whether the zoning change is approved will be released.
Now
1 Jun
1 Aug
15 Aug
1 Sep
Nov
Market research results available
Deadline to submit bid
Announcement of winning bid
Announcement of zoning referendum results
Based on the sequence of events in the timeline, we can draw a decision tree showing all the decisions and chance events. A more detailed decision tree with probabilities for each state of nature will be illustrated in the appendix.
Recommendations
1. If no market research information is available, the expected value of submitting the bid would be a profit of $0.05 million, whereas the payoff of not submitting the bid would be 0. Therefore, to maximize profit, Oceanview should submit the bid.
2. If the market research is conducted and it predicts the approval of zoning change, the expected value of submitting the bid would be a profit of $0.23 million, whereas the payoff of not submitting the bid would be 0. Hence, Oceanview should submit the bid.
3. If market research is conducted and it predicts that the zoning change will be rejected, the expected value of...

...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...

...I. Probability Theory
* A branch of mathematics concerned with the analysis of random phenomena. The outcome of a random event cannot be determined before it occurs, but it may be any one of several possible outcomes. The actual outcome is considered to be determined by chance.
* The word probability has several meanings in ordinary conversation. Two of these are particularly important for the development and applications of the mathematical theory ofprobability. One is the interpretation of probabilities as relative frequencies, for which simple games involving coins, cards, dice, and roulette wheels provide examples.
* It is the likeliness of an event happening based on all the possible outcomes. The ratio for the probability of an event 'P' occurring is P (event) = number of favorable outcomes divided by number of possible outcomes.
Example:
A coin is tossed on a standard 8×8 chessboard.
What is the theoretical probability that the coin lands on a black square?
Choices:
A. 0.5
B. 0.25
C. 0.42
D. 0.6
Correct answer: A
Solution:
Step 1: Theoretical probability = number of favorable outcomes / number of possible outcomes.
Step 2: The probability of the coin lands on the black square is 32.
Step 3: Total number of outcomes = 64.
Step 4: P (event) =
Step 5: == 0.5
Step 6: The theoretical probability that...