Probability-
describes the chance that an uncertain event will occur.

Empirical Probability - estimate that the event will happen based on how often the event occurs after collecting the data or running an experiment. It is based specifically on direct observation or experiences.

Empirical Probability Formula

P(E) = probability that an event, E, will occur.
Top = number of ways the specific event occurs.
Bottom = number of ways the experiment could occur.

Example: A survey was conducted to determine students' favorite color. Each student chose only one color. colorRedBlueBlackYellowPurpleOther
#1015358512
What is the probability that a student's favorite color being black? Answer: 35 out of the 85 students chose Black. The probability is
.

Theoretical Probability-Theoretical Probability: is the number of ways that an event can occur. You need to divide by the total number of outcomes. This is usually used with equally likely out comes.

Theoretical Probability Formula

P(E) = probability that an event, E, will occur.
n(E) = number of equally likely outcomes of E.
n(S) = number of equally likely outcomes of sample space S. Example 1: Find the probability of rolling a six on a fair die.
Answer: The sample space for rolling is die is 6 equally likely results: {1, 2, 3, 4, 5, 6}. The probability of rolling a 6 is one out of 6 or

.
Example 2: Find the probability of tossing a die and getting an odd number. Answer:
event E : tossing an odd number
outcomes in E: {1, 3, 5}
sample space S: {1, 2, 3, 4, 5, 6}

...BBA (Fall - 2014)
Business Statistics
Theory of Probability
Ahmad
Jalil Ansari
Business Head
Enterprise Solution Division
Random Process
In a random process we know that what outcomes or
events could happen; but we do not know which
particular outcome or event will happen. For
example tossing of coin, rolling of dice, roulette
wheel, changes in valuation in shares, demand of
particular product etc.
Probability
It is the numeric value representing the chance,
likelihood, or possibility a particular event will
occur
It is measured as the fraction between 0 & 1 (or 0%
&100%)
Probability can never exceed 1 and can never be negative
i.e. if P(x) is the probability of occurring event x then 0 ≤
P(x) ≤ 1
Probability = 0 No chance of occurrence of given event
(Impossible event)
Probability = 1 Given event will always occur (Certain
event)
Probability in Business
Betting / Speculation
Estimate the chances that the new product will be
accepted by customers?
Possibility that the planned target will be met
The likelihood that the share prices of the portfolio will
increase
Likelihood of surviving a person till a particular age
Likelihood of surviving a person suffering from a
particular disease
etc. etc.
Probability
It is the numeric value representing the
chance, likelihood, or possibility a particular
event will occur...

...Probability
1.) AE-2 List the enduring understandings for a content-area unit to be implemented over a three- to five- week time period. Explain how the enduring understandings serve to contextualize (add context or way of thinking to) the content-area standards.
Unit: Data and Probability
Time: 3 weeks max
Enduring Understanding:
“Student Will Be Able To:
- Know what probability is (chance, fairness, a way to observe our random world, the different representations)
- Know what the difference between experimental and theoreticalprobability is
- Be able to find the probability of a single event
- Be able to calculate the probability of sequential events, with and without replacement
- Understand what a fair game is and be able to determine if a game is fair
- Be able to make a game fair
- Be able to use different approaches (such as tree diagrams, area models, organized lists) to solve probability problems in life.
- Be able to predict the characteristics of an entire population from a representative sample
- Be able to analyze a representative sample for flaws in its selection
- Be able to create and interpret different statistical representations of data (bar graphs, line graphs, circle graphs, stem-and-leaf)
- Be able to choose an appropriate way to display various sets of data
- Know why the Fundamental Counting Principle...

...CHAPTER 3: PROBABILITY DISTRIBUTION
3.1
RANDOM VARIABLES AND PROBABILITY DISTRIBUTION
Random variables is a quantity resulting from an experiment that, by chance, can assume different values. Examples of random variables are the number of defective light bulbs produced during the week and the heights of the students is a class. Two types of random variables are discrete random variables and continuous random variable.
3.2
DISCRETE RANDOM VARIABLE
A random variable is called a discrete random variable if its set of posibble outcomes is countable. Probability distribution is a listing of all the outcomes of an experiment and the probability associated with each outcome. For example, the probability distribution of rolling a die once is as below: Outcome, x Probability, P(x) 1 1 6 2 1 6 3 1 6 4 1 6 5 1 6 6 1 6
The probability distribution for P(x) for a discrete random variable must satisfy two properties: 1. The values for the probabilities must be from 0 to 1; 0 ≤ ( ) ≤ 1 2. The sum for P(x) must be equal to 1; ∑ ( ) = 1
QMT200
3.2.1 FINDING MEAN AND VARIANCE Mean of X is also referred to as its “expected value”.
= ( ) Where: = ∑[ ( )]
( )=
= (
) − [ ( )]
(
)=
[
( )] = ( )
Example 1 An experiment consists of tossing two coins simultaneously. Write down the sample space. If X is the number of tails observed,...

...chapter, you will be able to ONEDefine probability. TWO Describe the classical, empirical, and subjective approaches to probability. THREEUnderstand the terms experiment, event, outcome, permutation, and combination. FOURDefine the terms conditional probability and joint probability. FIVE Calculate probabilities applying the rules of addition and multiplication. SIXUse a tree diagram to organize and compute probabilities. SEVEN Calculate a probability using Bayes theorem. What is probability There is really no answer to this question. Some people think of it as limiting frequency. That is, to say that the probability of getting heads when a coin is tossed means that, if the coin is tossed many times, it is likely to come down heads about half the time. But if you toss a coin 1000 times, you are not likely to get exactly 500 heads. You wouldnt be surprised to get only 495. But what about 450, or 100 Some people would say that you can work out probability by physical arguments, like the one we used for a fair coin. But this argument doesnt work in all cases, and it doesnt explain what probability means. Some people say it is subjective. You say that the probability of heads in a coin toss is 12 because you have no reason for thinking either heads or tails more likely you might change your...

...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....

...Probability theory
Probability: A numerical measure of the chance that an event will occur.
Experiment: A process that generates well defined outcomes.
Sample space: The set of all experimental outcomes.
Sample point: An element of the sample space. A sample point represents an experimental outcome.
Tree diagram: A graphical representation that helps in visualizing a multiple step experiment.
Classical method: A method of assigningprobabilities that is appropriate when all the experimental outcomes are equally likely.
Relative frequency method: A method of assigning probabilities that is appropriate when data are available to estimate the proportion of the time the experimental outcome will occur if the experiment is repeated large number of times.
Subjective method: A method of assigning probabilities on judgment.
Event: A collection of sample points.
Complement of A : The event consisting of all sample points that are not in A.
Venn diagram: A graphical representation for showing symbolically the sample space and operations involving events in which the sample space is represented by a rectangle and events are represented as circles within the sample space.
Union of A and B : The event consisting of all sample points belonging to A or B or both.
Intersection of A and B : The event containing the sample points belonging to both A and B.
Conditional probabilities: the...

...Probable Probability;
Rolling Dice
Statistics is based upon based upon common sense and logic, in a complex data. Probability is just one of the many topics in statistical mathematics. It is used in our daily life, all over the world. Even games, require taking a chance and using probability to determine the predicted outcomes.
Probability is the measure of how often a particular event will happen if something is done repeatedly, (596 Webster’s Dictionary). You cannot determine any events that will happen in the future, because there is always a chance that something odd will happen, (Linn 39-40).
Probability originally started for the purpose and attempt to analyze games of chance. Probability is also used in determining the outcomes of an experiment. Sample space is the collection of all results. Probability is a way to assign every event a value between zero and one.
What is the probability of rolling a pair of dice, or a deck of cards, or a jar of marbles? What is the probability of conceiving a boy or a girl? Many more are determined by the usage of the probability method.
Probability is used to represent the likelihood that odds of winning a random drawing chance of rolling a seven when rolling two dice.
When rolling a six-sided die there are six possible events...

...Lecture
In the current lecture:
Introduction to Probability
Definition and Basic concepts of probability
Some basic questions related to probability
Laws of probability
Conditional probability
Independent and Dependent Events
Related Examples
2
Probability
Probability (or likelihood) is a measure or estimation of how likely it is that
something will happen or that a statement is true.
For example, it is very likely to rain today or I have a fair chance of passing
annual examination or A will probably win a prize etc.
In each of these statements the natural state of likelihood is expressed.
Probabilities are given a value between 0 (0% chance or will not happen) and 1
(100% chance or will happen). The higher the degree of probability, the more
likely the event is to happen, or, in a longer series of samples, the greater the
number of times such event is expected to happen.
Probability
is
used
widely
in
different
fields
such
as:
mathematics, statistics, economics, management, finance, operation research,
sociology, psychology, astronomy, physics, engineering, gambling and artificial
intelligence/machine learning to, for example, draw inferences about the
expected frequency of events.
3
ProbabilityProbability theory is best understood through the application of the modern
set...

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