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 that correspond to the six face of the die that contains either one, two, three, four, five, and six dots. Rolling a die and turning up an even number of dots would be one example, (2, 4, and 6).

Probabilities are formally written as decimals in the range of 0-1. Meaning the event occurred. Meaning a certain event must occur. When rolling a die, getting a seven, eight, or nine or more dots is an impossible event. Two dots or fewer are a certain event.

Probabilities can also be written informally in percentage for example 50-50-%. There is no negative probability chance. The probability of getting a face that has two dots on a die is 1/6(1....

...Probability Games
Walter J Mahoney
MTH 157
1/20/2013
Andrea Hayes
Probability is a fascinating math concept. It can be applied in many aspects of our students’ daily lives. As the world of technology continues to grow, teaching of many math concepts can be done in the classroom and reinforced by math learning websites. The coin flip and roll dice games that we looked at are a nice tool to show our students the concept of probability in visual form.
The coin flip game showed the probability of two results either heads or tails. It is less complex because it only has two possible results, the probability of a heads or tails coming up when flipped is 50% or one out of two chance. In the game, you control the number of flips of the coin and the results are noted and percentage is giving to you. In my results of 20 single flips, the results were 50% heads and 50% tails. But when I used the auto flip button for another 20,000 flips, the results were 50.11% heads and 49.89% tails. There was a historical button which shows historical data with results of 50% heads and 50% tails. It is a nice visual tool to explain the results of the...

...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 theoretical probability 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 works and be...

...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...

...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 computeprobabilities. 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 view if you knew...

...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...

...of observations, which gives each observation equal weight, the mean of a random variable weights each outcome xi according to its probability, pi. The mean also of a random variable provides the long-run average of the variable, or the expected average outcome over many observations.The common symbol for the mean (also known as the expected value of X) is , formally defined by
Variance - The variance of a discrete random variable X measures the spread, or variability, of the distribution, and is defined by
The standard deviation is the square root of the variance.
Expectation - The expected value (or mean) of X, where X is a discrete random variable, is a weighted average of the possible values that X can take, each value being weighted according to the probability of that event occurring. The expected value of X is usually written as E(X) or m.
E(X) = S x P(X = x)
So the expected value is the sum of: [(each of the possible outcomes) × (the probability of the outcome occurring)].In more concrete terms, the expectation is what you would expect the outcome of an experiment to be on average.
2. Define the following;
a) Binomial Distribution - is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probability p. Therewith the probability of an event is defined by its binomial...

...PROBABILITY DISTRIBUTION
In the world of statistics, we are introduced to the concept of probability. On page 146 of our text, it defines probability as "a value between zero and one, inclusive, describing the relative possibility (chance or likelihood) an event will occur" (Lind, 2012). When we think about how much this concept pops up within our daily lives, we might be shocked to find the results. Oftentimes, we do not think in these terms, but imagine what the probability of us getting behind the wheel of a car twice a day, Monday through Friday, and arriving at work and home safely. Thankfully, the probability for me has been 'one'! This means that up to this point I have made it to work and returned home every day without getting into an accident. While probability might have one outcome with one set of circumstances, this does not mean it will always turn out that way. Using the same example, just because I have arrived at work every day without getting into an accident, this does not mean it will always be true. As I confess with my words, and pray it does stay the same, probability tells me there is room for a different outcome.
In business, we often look at the probability of success or financial gain when making a decision. There are several things to take into consideration such as the experiment, potential outcomes, and possible events. An...

...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...

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