A Philosophical Essay On Probabilities

Probability Concepts
Probability Concepts Introduction Probability concepts describe how uncertainty can be quantified,
and it measures the possibility or impossibility of occurrence of a given event. Probability is the
chance of a particular outcome, out of a number of times possible outcomes occurring for a certain
event. These concepts help in making inferences about situations and to quantify the uncertainty of
future events. It is, therefore, useful to review basic concepts and laws of probability to understand
how to manage uncertainty. Probability concepts help to interpret probabilities from two–way pivot
tales. They are also useful in understanding probability, in statistical analysis, and apply the rules
of probability in the empirical data. Probability concepts Probability presents the intellectual
machinery to deal with uncertainty in business or personal life. With the concept of present value
and courteous evaluation skills, it becomes easy to deal with situations. Probabilities are broadly
of two types, subjective and objective probability. Subjective probability of an event is based on
an educated guess, pure intuition or expert opinion. Subjective probability is not based on
statistically verified data, and it is not extensively used in statistical analysis. According to
subjective probability or personalistic concept, the probability of an event is the degree of belief, or
the degree of confidence one places on the occurrence of an event according to the available
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John Smith The Probability Of Life
The Probability of Life as an Argument for a Designer In response to the argument from life, Smith
claims that "the argument from life again presents us with a false alternative between design and
chance... in fact, there is neither; we have with life what we have with every other natural
phenomenon: natural causes operating according to natural necessity" (270). Smith further claims
that even if he concedes the improbability of life, that does not prove anything except "that an
extraordinary occurrence has taken place" (270). However, his arguments are problematic because
while he refutes the argument from life as a proof of design he does not refute it as an inference to
the best explanation. For this reason, many of his arguments are irrelevant...show more content...
However, this argument does not carry much strength because it fails to recognize the difference
between the complexity of a rock and the complexity of life in relation to the conditions which the
universe must meet in order for each to exist. While there are many conditions which the universe
must meet in order to make life possible (the existence of carbon, water, and precise physical
constants), a rock only requires the existence of the certain elements which make up a rock and some
force to hold these elements together, meaning that a universe in which rocks are able to exist is
far more probable than a universe in which life is able to exist. For this reason, it is not
unreasonable to hold that design is necessary for life but not necessary for rocks and dirt.
Furthermore, the argument from life argues for the probability of a designer of the universe, not
for the probability of a "god of life"; therefore, rather than arguing for a "rock god" under the same
principles, one could argue that probability indicates that the universe was designed (by a designer,
not necessarily a "rock god") so that rocks might exist. This would be a completely rational belief
for the same reasons that believing that life was the result of design is

Probability and Statistics
University of Perpetual Help System Dalta Molino Campus Molino III, Bacoor City Probability and
Statistics LAGERA, Einar John A. Table of Contents Simple Correlation Analysis
................................................................................................. 1 Introduction
.................................................................................................................................................................
1 What is Correlation?
............................................................................................................................................ 1 Discussion
starts here(Simple Correlation Analysis)...show more content...
Before we have those chit–chats about Simple Correlation Analysis, let me define first what
correlation is and its features. What is Correlation? Correlation is a measure of the relation between
two or more variables. The measurement scales used should be at least interval scales, but other
correlation coefficients are available to handle other types of data. Correlation coefficients can range
from –1.00 to +1.00. The value of –1.00 represents a perfect negative correlation while a value of
+1.00 represents a perfect positive correlation. A value of 0.00 represents a lack of correlation.
Correlations are very useful because they can indicate a predictive relationship that can be
exploited in practice. For example, an electrical utility may produce less power on a mild day based
on the correlation between electricity demand and weather. In this example there is a causal
relationship, because extreme weather causes people to use more electricity for heating or cooling;
however, statistical dependence is not sufficient to demonstrate the presence of such a causal
relationship (i.e., Correlation does not imply causation). Correlation often is abused. You need to
show that one variable actually is affecting another variable. The parameter being measure is ПЃ
(rho)

Philosophy of Ethics Essay
The word "ethics" comes from Greek ethikas meaning character. Today, we use ethics to describe the
normative standard of behavior. The history of philosophical ethics has been broken up into five
rational methods: Virtue, Traditional, Modern, and Post–Modern Ethics. Within these periods, the
philosophy of ethics changed along with the changes being made within society. The first rational
method is Virtue Ethics. The major philosophers during this period were materialists such as Plato,
Aristotle, Epicurus, and Plutarch. Greek were concerned with finding eudaimonia meaning the good
life, but what is the good life? Known as the greatest Western philosopher, Plato developed the
Cardinal Virtues: Justice, Courage, Moderation, and...show more content...
One of the last major philosophers of Virtue Ethics was Plutarch who advocated virtue but disagreed
with Epicurus because he believed there was no true pleasure. At this same time, between 400 B.C.–
40 B.C. Stoic philosophers such Cicero, who combined the philosophies of Aristotle and Plato,
developed his idea on ethics and how everyone has a duty and should imitate virtue for others. He
said duty has two points which are to achieve the Supreme Good, and follow the rules for daily
living. Cicero was a strong believer in rationality incorporated Plato's Cardinal Virtues into his three
rules of conduct: master desires through reason, know true value of goals and be moderate in
actions and lifestyle. Following Virtue Ethics, a major shift occurred in thinking. The philosophers
of Virtue Ethics were materialists and believed we only have what we have and after death, we have
nothing. Traditional Ethics shifted the focus on religion once it began to spread. Also known as
Biblical Ethics, philosophers started a systematic study of Biblical themes and principles surrounding
ethics and morality. St. Augustine was trained as a philosopher and combines his understanding of
the Bible to ethics by answering the same question as Plato and Aristotle did, "What is the highest
good?" He answered this question with happiness just like Aristotle but since Aristotle

The Rationality of Probabilities for Actions in Decision Theory
ABSTRACT: Spohn's decision model, an advancement of Fishburn's theory, is valuable for making
explicit the principle used also by other thinkers that 'any adequate quantitative decision model must
not explicitly or implicitly contain any subjective probabilities for acts.' This principle is not used in
the decision theories of Jeffrey or of Luce and Krantz. According to Spohn, this principle is
important because it has effects on the term of action, on Newcomb's problem, and on the theory of
causality and the freedom of the will. On the one hand, I will argue against Spohn with Jeffrey that
the principle has to be given up. On the other, I will try to argue against...show more content...
In 1969 Robert Nozick introduced Newcomb's problem to the philosophic community as a
conflict between the principle of expected utility maximization and the principle of dominance.
Nozick's introduction led to a "Newcombmania" (Levi 1982), because philosophers have
decisively different opinions about the correct solution to this problem. The "Newcombmania"
showed itself in the development of causal and evidential decision theories and other proposals.
Because the evidential theories (for example Jeffrey 1965, 1983) do not use the principle, they
cannot give a solution to Newcomb's problem in case you accept the principle. The causal theories
which use subjunctive conditionals (for example Lewis 1981) are problematical, because they still
have to provide a logic of subjunctive conditionals, a probability theory for subjunctive conditionals
and a corresponding decision theory. Because Skyrms' (1980) causal theory and Kyburg's (1980)
proposal of epistemic vs. stochastic independence also don't use the principle, only Spohn's solution
(1978) to Newcomb's problem is left. This solution which recommends taking both boxes is valuable
for its simplicity in contrast to the theories with subjunctive conditionals. According to Spohn it is a
mistake to use probabilities conditionalized on actions for the results of the prediction, if the
prediction is earlier than the choice. According to Spohn it is right that the

Probability in Daily Life
Chapter 1
The Probability in Everyday Life
In This Chapter
Recognizing the prevalence and impact of probability in your everyday life
Taking different approaches to finding probabilities
Steering clear of common probability misconceptions
You've heard it, thought it, and said it before: "What are the odds of that happening?" Someone wins
the lottery not once, but twice. You accidentally run into a friend you haven't seen since high school
during a vacation in
Florida. A cop pulls you over the one time you forget to put your seatbelt on.
And you wonder . . . what are the odds of this happening? That's what this book is about: figuring,
interpreting, and understanding how to quantify the random phenomena of life. But it also helps you
...show more content...
This probability means that in the long term (over thousands of tickets), 10 percent of all instant
lottery tickets purchased for this game will win a prize, and 90 percent won't. It doesn't mean that if
you buy 10 tickets, one of them will automatically win.
10 Part I: The Certainty of Uncertainty: Probability Basics
If you buy many sets of 10 tickets, on average, 10 percent of your tickets will win, but sometimes a
group of 10 has multiple winners, and sometimes it has no winners. The winners are mixed up
amongst the total population of tickets.
If you buy exactly 10 tickets, each with a 10 percent chance of winning, you might expect a high
chance of winning at least one prize. But the chance of you winning at least one prize with those 10
tickets is actually only 65 percent, and the chance of winning nothing is 35 percent. (I calculate this
probability with the binomial model; see Chapter 8).
Pondering political affiliation
You can use the following example as an illustration of the limitation of probability– namely that
actual probability often applies to the percentage of a large group. Suppose you know that 60
percent of the people in your community are Democrats, 30 percent are Republicans, and the
remaining 10 percent are Independents or have another political affiliation. If you randomly select
one person from your community, what's the chance the person is a Democrat?
The chance is 60 percent. You can't say that

Pascal's Wager: A Philosophical Argument
Pascal's wager is indeed a unique piece of philosophical argument and it sure has an enormous
impact on countless philosophers as well as believers. Its historical achievement can never be
unrecognized. However, after having read through and analyzing his wager, I actually found it less
persuasive in a logic manner and somehow discriminatory from my personal point of view. The
wager is neatly–structured and clearly explained, each conclusion is supported by the premises and
they all make sense from a structural–level point of view. Yet, it is a bold attempt to clarifybelief in
God not with an appeal to evidence for his existence but rather with an appeal to self–interest.
Pascal's wager seeks to justify Christian faith by considering...show more content...
On the contrary, I think passion is a critical component to form a belief. Passion is one's free will,
it is one's desire which comes from deep down of its heart. Take myself as an example, I am
passionate about knowing people with unique and interesting stories, thus I believe there are people
out who meet my criteria. Belief isn't formed all of a sudden, it sure doesn't from stupefying yourself

Different Research Philosophies Essay
Working on a project has always been requiring doing a deep philosophical framework in order to
be as informative and interesting to be read as it can. bring the best results. Moreover, putting a
philosophical framework in projects is supposed to be a critical issue. In addition to this, in order
to show clearly the aim as well as the focus of the project, each step must be appropriate, and 'fit' if
we want to talk with the language of modern research philosophies. Projects should also be
characterized by a logical cohesion, so philosophical approaches should be placed correctly while
organizing the plan for a project.
To start with, this essay discusses the different research philosophies as well as gives many
different authors' views. First of all, in every kind of project, philosophy should be put into it.
Philosophy is the use of nonconcrete ideas and views that notify our study (Creswell, page 16).
Research philosophy can be defined as the development of the research background, research
knowledge and its nature (Saunders and Thornhill, 2007). Research philosophy is also defined
with the help of research paradigm. In the words of Cohen, Manion and Morrison (2000), research
paradigm can be defined as the broad framework, which comprises perception, beliefs and
understanding of several theories and practices that are used to conduct a research. It can also be
characterized as a precise procedure, which involves various steps through which a researcher
creates a

Math is present in everyday life and can be used in any situation. Probability is a mathematical
concept in which people use more often then they know. In my case I have used probability more
outside of math class then I realized. Probability consists of multiple concepts mostly about the
occurrence of events. I will explain in more detail how probability is essential in a game degree
and how it is used properly in order to determine events. First, Probability and how it is used.
Probability is used to determine the occurrence of an event in which can be applied in any aspect
of life. An example would be the probability of it raining today. Using factors such as wind, cloud
coverage, etc., weather forecaster are able to predict the likeness of it to rain and convert it into a
percentage. So if there was 50% chance it was going to rain the probability would be ВЅ. Probability
can also be applied in more personal situations. According to the article "NEVER SAY NEVER"
by David J. Hand, the weird coincidences in life that people don't expect or is very unlikely are
actually very likely or almost certain if given enough opportunities. An example of this would be
winning the lottery. If someone were to buy 100,000 lottery tickets the chance of them winning is
much greater than someone who only bought 10 tickets. If that person bought all the lottery tickets
they were guaranteed to win because of one out millions of tickets would have the winning number
on it. David J. Hand also

Value of Philosophy Essay
Philosophy is the study of examining and thinking about questionable ethical problems and/or
generally accepted certainties. Philosophy aims at knowledge that combines a variety of academic
fields as well as convictions, prejudices and beliefs.
What is Russell's essay about? Present Russell's position in your own words.
Bertrand Russell's essay addresses many issues concerning philosophy. In the writing, he states
philosophy's nature, value, and criticisms. The essay explains these aspects of the study of
philosophy in relatively different ways. The main idea for establishing value in his essay is by
explaining how it is best obtained, and its effect on other people. The essay continues with his
criticisms of those who opposed...show more content...
It states that even though philosophy doesn't give us a certainty of true answers, it suggests many
possibilities which enlarge our thoughts and free them from tyranny of custom. He also supports
the idea that philosophy is beneficial because it "enriches intellectual imagination". The essay
brings up the points of the practical man, and why they are at a loss of intellectual imagination
because they don't explore the unknown by viewing life as simple. As evidence, he uses an
example of mass disease and poverty of a society. The theory is that in those conditions, there would
still be much to be improved to produce a valuable society. Even if the society has the proper food
supplies, they need the 'goods of the mind' (knowledge) to build a well–governed society. He
believes practical men undermine that aspect, thereby explaining their lack of intellectual
imagination. The next argument is that philosophy saves us from convictions, prejudices, and
cultural beliefs. The affect that that has on a person is to open up a fresh prospective with very
little bias. He believed for this to be beneficial to people socially, by developing empathy which
helps you understand others points of view. That theory goes hand–in–hand and gives a fine segway
to his fourth and final argument of "the freedom and equity learned from philosophical
contemplation reflecting in your personality (action and emotion). The

Theorems of Probability
UNIT 2 THEOREMS
Structure
2.1 Introduction
Objectives
PROBABILITY
2.2 Some Elementary Theorems
2.3 General Addition Rule
2.4 Conditional Probability and Independence
2.4.1 Conditional Probability 2.4.2 Independent Events and MultiplicationRule 2.4.3 Theorem of
Total Probability and Bayes Theorem
2.5 Summary
2.1 INTRODUCTION
You have already learnt about probability axioms and ways to evaluate probability of events in
some simple cases. In this unit, we discuss ways to evaluate the probability of combination of
events. For this, we derive the addition rule which deals with the probability of union of two events
and the multiplication rule which deals with thc probability of intersection of two events. Two
important...show more content...
Find the probability that a person stopping at the gas station will have (i) his tyres or his oil
checked and (ii) will have neither his tyres nor his oil checked.
2 3 GENERAL ADDITION RULE .
You have already learnt the addition rule ( Theorem 3 ) for finding the probability of occurrence of
at least one of the two given events. In this section, you will learn the general addition rule which
will help you to evaluate the probability of occurrence of at least one of the given n events. If the a
events are denoted by A1 ,A2 ,..An then our aim is to find a formula for evaluating P (A1 U A2 U ...
U An ) . For this, let us first take 3 eventsA ,B and C and use Theorem 3 to find the expression for P
(A U B U C ) .
Theorem 4 : If A ,B and C are any three events, then
P(AUBUC) = P(A)+P(B)+P(C)–P(AnB)
Tbcorem~ Probability of
i

L
1
Proof : Let us denote B U C by D and therefore
t
where equation (2.9) follows because of Theorem 3. Also using Theorem 3 again,
P(D)
=
P(BUC)
–
P(B)+P(C)–P(BnC)
and
Substituting for P ( D ) and P ( A
n D ) in equation (2.9) we obtain
which proves

Probability Theory In Health And Social Care
Probability Probability is the likelihood that a certain outcome will occur. Flipping a coin 10
times, and trying to predict the odds or chances of getting heads more than tails is a good
example of probability. The history of probability seems to have come from the 1650's over a
game of dice. Two French mathematicians, Blaise Pascal and Pierre de Fermat shared
correspondence with one another over the odds of getting a double six over the course of 24 dice
rolls (Devlin, 2010). This thought process laid the foundation for probability theory's fundamental
principles. Probability is calculated as P(A) = Number of outcomes that favor A/the number of
outcomes. This is easiest to understand when looking at the example of a coin toss. There are two
outcomes, so if you look at the outcome of heads over tails it would be A =1/2, and A would be
0.5. Working on predicting the outcomes in healthcare can yield several benefits; once trends of
disease prevalence in a certain subculture, or socioeconomic group have been established through
probability theory a healthcare provider can work on focusing a specific healthcare needs and
prevention for that group. This approach would be very cost effective, as the healthcare provider can
cover a large amount of the population with minimal effort. Additionally, once the trends have been
identified, there would...show more content...
These two interpretations are at odds with one another, because objective interpretation deals with
the frequency of an event and how likely it is that it will be repeated, whereas subjective
interpretation is based off of an individual's personal judgement on a specific event reoccurring.
Subjective interpretation has no formal calculations, and relies on a person's personal perspective
whereas objective interpretation is based solely on the numerical outcome (Shmaliy, 2012).
Outcomes of Survey: Tested and

The Multiverse Theory
The argument suggesting life existing on other Earth–like planets has been present since man first
looked into space and questioned his own existence and the existence of others like him. Today there
are many theories on the existence of intelligent life elsewhere in the universe, but only one theory
goes beyond them and into an even larger realm. The contents of this theory, known as the "
multiverse" theory, suggest that humans on Earth live within one universe of many others that reside
within a primordial vacuum containing many other universes (Jenkins and Perez). Each of these
universes possesses potentially different natural constants and physical laws that govern them
differently, thus calling forth some logical questions. First,...show more content...
Slightly shifting any of these variables individually can result in the destruction of life or the
inability for life to form in the first place. However such shifts can, if varied simultaneously with
another constant of principle, result in other plausible universes that render carbon, hydrogen, and
oxygen–like atoms, which could eventually create a form of intelligent life somewhat resembling
humans (Jenkins and Perez, 47). Based on the experimentation performed by physicists Alejandro
Jenkins and Gilad Perez, there are four fundamental forces that enable life within our universe,
without which humans would not exist. They consist of the strong nuclear force, electromagnetic
force, gravity, and weak nuclear force. Because the other three forces are so vital to the existence of
life, the two decided to eliminate the weak nuclear force and study the resulting possibilities via
simulations and graphical reasoning. Their experiment created graphs showing two variables, one
per axis. They showed that there is a "small range [within each variable that is] congenial to life"
(Jenkins and Perez), and by combining two variables, the range supporting life increases. This means
that if other universes do exist in an infinite quantity, as this theory asserts, the probability that
intelligent life exists within them is high. Though not all possess conditions that support organic
molecules

Questions on Probability
1. A card is drawn at random from a standard 52–card deck. Find the probability that the card is not a
queen. 52 card 4 queens = 48 cards that are not queens. 48/52 = 12/13 or 0.923 = 92.3% probability
of not drawing a queen from a standard 52–card deck. 2. Two fair dice are rolled. Find the
probability that the sum of the two numbers is not greater than 5. 1+1, 1+2, 1+3, 1+4, 2+1, 2+2,
2+3, 3+1, 3+2, 4+1 are the 10 possible occurrences of two fair dice rolling numbers not greater than
5. With each dice having 6 sides there are 6*6=36 possible outcomes. So there is a 10/36 = 5/18 or
0.625 = 62.5% probability of two fair dice rolling a number combination not greater than 5. 3. This
spinner is spun 36 times. The spinner landed on A 6 times, B on 21 times, and on C 9 times.
Compute the empirical probability that the spinner will land on B. [pic] A=6, B=21, C=9. The
empirical probability of the spinner landing on B is 21/36 = 7/12 or 0.583 = 58.3% 4. If a person is
randomly selected, find the probability that his or her birthday is not in May. Ignore leap years.
There are 31 days in May and 365 days in a year. 365 31 = 334 days that are not in May. 334/365 or
0.915 = 91.5% probability that his birthday is not in May. 5. The chart below gives the number of
vehicle tags sold in each city. One car is selected at random from the cars with vehicle tags from
these cities. What is the probability that this car is from Salem? There are 1773 occurrences of a car
being from Salem

Analysis Of Noonan's Argument From Probabilities
Araka Bell
HUM Ethics MOD 2
Indiana Tech
September 11, 2015
1. What is Noonan's "Argument from Probabilities?" How does this argument work, and what does
he think it implies about the morality or immorality of abortion?
John Noonan begins his essay by rejecting several answers to the questions of when does life begin,
he uses a word that the courts specifically did not use which is viability. Another is ensoulment. He
uses what he called Catholic theology to answer that question plainly stating that if you are
conceived by human parents then you are human. He reviewed the weakness of arguments about
abortion to leave his position as the only one that made sense.
He used five points or distinctions to convey his beliefs. Viability, thefetus...show more content...
I specify Christians because I am not familiar with the rights or wrongs of abortions in other
religions. Christians use the bible for teaching and reproof. The bible is not confusing when it
comes to this issue. In the new world translation of the bible the psalmist states "Your eyes saw
even the embryo of me." (Psalm 139:16) There are several instances where God has condemned the
murder of an unborn child. In Exodus 21: 22–23 22 there is an illustration and condemnation of
evens that cause the accidental harm of a pregnant woman. It states "If men should struggle with
each other and they hurt a pregnant woman and she gives birth prematurely but no fatality results,
the offender must pay the damages imposed on him by the husband of the woman; and he must
pay it through the judges. 23 But if a fatality does occur, then you must give life for life, God stated
that a person would be called to account for injuring an unborn child. So, in his eyes, killing an
unborn child is murder. (Ex. 21:22,

A philosophical analysis of an idea presented by Ludwig Wittgenstein in On Certainty Introduction
Countless philosophers, from centuries ago to modern times, have investigated the concept of
inherited ideas. Some of the more daunting questions on the subject seem to be: From where do
these ideas originate? Can we trust them? Do they serve as an objective foundation for the rest of
our judgments, or are they in fact mere judgments themselves? Ludwig Wittgenstein addresses such
questions in his written work On Certainty, and deduces that in some cases, an inherited idea is "so
anchored [in me] that I cannot touch it" (no. 103). This paper will examine the definition of this
idea and the argument that lies behind it, while also addressing the various objections that could be
made to such an argument. Explanation of Idea In On Certainty, Wittgenstein arrives at the
conclusion that "some of my ideas are so anchored in me that I cannot touch them." The key
message Wittgenstein is conveying here is that certain ideas are inherited, innate for everyone. The
term "anchored", in its literal sense, refers to watercraft being held securely in a fixed spot by aid
of a curved, weighted implement to which it is connected. In using this term, Wittgenstein creates
the imagery of our intellect, our perception, being like a sea, and our ideas like ships. This
illustration suggests that some of the ideas we have are in motion, changing as a result of our
experiences and investigations

Philosophy in Mathematics Essay
Philosophy in Mathematics
Mathematics has contributed to the alteration of technology over many years. The most noticeable
mathematical technology is the evolution of the abacus to the many variations of the calculator.
Some people argue that the changes in technology have been for the better while others argue they
have been for the worse. While this paper does not address specifically technology, this paper rather
addresses influential persons in philosophy to the field of mathematics. In order to understand the
impact of mathematics, this paper will delve into the three philosophers of the past who have
contributed to this academic. In this paper, I will cover the views of three philosophers of
mathematics encompassing their...show more content...
At this time it was customary for men of his stature to choose from church or army, which he would
serve. Choosing the latter position, Descartes joined the army in 1617.
In an event of chance, Descartes stumbled upon Isaac Beeckman, head of the Dutch College at Dort,
who would translate a sign off the streets. This sign was in actuality a challenge to anyone to solve a
geometrical problem (Wilkins, D.). Within a few hours, with help from Descartes' respect and
appreciation of mathematics, he found a solution and a friendship was formed between Beeckman
and Descartes. This unexpected turn of events fueled Descartes' contempt of his life in the army;
but due to family influence and tradition, he remained a soldier until 1621 (Wilkins, D.). Descartes
was 25 years old.
The next couple of years found him relocated all around Europe until he settles in Paris in 1626. In
the five years from when he left the army until his alighting in Paris, Descartes had devoted his life
to the study of pure mathematics. There, in Paris, Descartes would live for two years until Cardinal
de Berulle, founder of the Oratorians, urged on Descartes the duty of "devoting his life to the
examination of truth." (Wilkins, D.). Now 1628, Descartes moved again, this time to Holland, to
secure himself from interruption. He would spend the next twenty years in Holland, focusing on
philosophy and mathematics.
His time in Holland

In Elementary school, students are unaware of the predictions and probabilities they make on a daily
basis. However, when teachers explain predictions and probability in mathematics classes, most
students leave their reasoning behind in hopes of finding the correct and exact answer to questions.
In the article, "Predictions and Probability" author Sue McMillen provides readers with open–ended
investigations to help teachers with their mathematics lesson plans dealing with probability and
predictions. The open–ended investigations McMillen offers to readers builds problem solving and
reasoning skills, communication skills, as well as teaching students to connect math concepts and
principles to real–world problems. The author also explained

Mathematics: Probability
Contents| Page| Part 1| 2| Part 2| 5| Part 3| 6| Part 4| 8| Part 5| 10| Further Exploration| 13|
Conclusion| 14| Reflection| 15|
Part 1
a) Introduction
The word Probability derives from probity, a measure of the authority of a witness in a legal case in
Europe, and often correlated with the witness 's nobility. In a sense, this differs much from the
modern meaning of probability, which, in contrast, is used as a measure of the weight of empirical
evidence, and is arrived at from inductive reasoning and statistical inference.
A short history of Probability Theory............
The branch of mathematics known as probability theory was inspired by gambling problems. The
earliest work was...show more content...
Another significant application and importance of probability theory in everyday life is reliability.
Many consumer products, such as automobiles and consumer electronics, utilize reliability theory in
the design of the product in order to reduce the probability of failure. The probability of failure may
be closely associated with the product 's warranty.
Gambling is also usually associated with probability theory. This is a good example of the
probability theory as this is what the bookies use to set the odds for gambling.
b) Differences between Theoretical and Empirical Probabilities
Empirical probability, also known as relative frequency, or experimental probability, is the ratio of
the number favourable outcomes to the total number of trials,[1][2] not in a sample space but in an
actual sequence of experiments. In a more general sense, empirical probability estimates probabilities
from experience and observation.[3] Empirical probability is the data that has been proven through
trial and error such as the statics on the accidents that involve driving while under the influence.
Even the proven data for deaths that are smoking related.
A theoretical probability, however, is one that is calculated based on theory, i.e., without running any
experiments. The theoretical probability is like guessing and taking a chance you are right much
like playing a game of cards you are taking that chance you have the better hand.
Theoretical

Common Themes Of Probability And Outcome
Probability and Outcome
A number of years ago in 1978 there was a movie that starred Warren Beatty. It was called Heaven
Can Wait. Throughout the film, there was a common theme of probability and outcome. It kept
showing how the probability of something happening seemed almost certain however; the outcome
was different in many cases than one would have thought it to be.(Beatty, Beatty, & Henry, 1978)
When I took my first statistics class, my professor on the first day asked a question of us all. He
wanted to know how many people thought that out of our class of about 25 students that two of us
would have the same birthday not including the year of birth. He left the room for five minutes as
we all wrote down our birthdays on a slip of

A Philosophical Essay On Probabilities

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A Philosophical Essay On Probabilities