The document discusses various aspects of counting, probability, and expected value through a series of mathematical problems and scenarios, alongside a detailed examination of the American education system's shortcomings, particularly regarding biases faced by Black students from White teachers. It highlights that while the U.S. education system aims for inclusivity, significant disparities exist in educational opportunities and outcomes, often influenced by socioeconomic factors and implicit biases. The text emphasizes the need for reform to address these biases and their impacts on student achievement.

1. Module 4-5 Counting, Probability, and Expected Value
Show all work to receive credit. Any written questions should
be at least 3 sentences long.
Counting
1. A gift-wrapping store has 8 shapes of boxes, 14 types of
wrapping paper, and 12 different bows. How many different
gift-wrapping options are available at this store?
2. Four friends go to the movies. How many different ways can
they sit in a row?
3. You are creating a 4-letter password using only the 26
lowercase letters from the alphabet. How many unique
passwords could you create (assuming the password does not
need to spell a real word) if:
a. Repeating letters is allowed?
b. Repeating letters are not allowed?
c. What are some passwords that are possible in a. that are not
possible in b.? What are some passwords that are possible in
either scenario?
4. Which of the following do I have to check before using the
nPr? There may be more than one correct answer:
MTH 101
a.

2. b. Repeating is allowed
c. Repeating is not allowed
d. The order matters
e. The order does not matter
Explain in a complete sentence why you chose the options for
the previous question:
5. Which of the following do I have to check before using nCr?
There may be more than one correct answer:
MTH 101
a.
b. Repeating is allowed
c. Repeating is not allowed
d. The order matters
e. The order does not matter
6.
Explain in a complete sentence why you chose the options for
the previous question:
7. Two people out of a group of 75 will win tickets to an
upcoming concert. How many different groups of two are
possible?
8. Barry is hosting a Super Bowl party and offers 7 different
kinds of chip dip. If a party goer can choose any number of chip
dips for their chips, how many chip dip combinations are
possible?

3. 9. There are 30 students in the classroom competing for
classroom prizes. Only the first two students whose name is
drawn will win a prize. The first student wins 5 bonus points
and the second student wins 2 bonus points, both on the
upcoming test. If you are one of the 30 students, what is the
probability you will win the top prize and your best friend wins
the second prize?
Probability and Odds
Answer all questions with a fraction in lowest terms. If you’d
like, you can also write them as a percent.
If you draw one card at random, what is the probability that
card is a(n)…
9. Heart?
10. 7 of diamonds?
11. face card or a club?
Given the card is a club, what is the probability a card drawn at
random will be a(n)…
12. 8?
13. 10 or ace?
You are choosing two cards, without replacing the first card.
What is the probability you choose…
14. a 7 then a 3?

4. 15. two consecutive fours?
16. two consecutive diamonds?
You are choosing two cards, replacing the first card in the deck
after it has been drawn. What is the probability you choose…
17. a 7 then a 3?
18. two consecutive fours?
19. two consecutive diamonds?
20. A card is drawn from a standard deck of 52 cards, and then
replaced in the deck. Find the probability that at least one king
is drawn by the fourth draw. Round your answer to two decimal
places. Do not round until your final calculation.
21. Bill and Sam are playing a game where they roll a die and
draw a card from a deck. What is the probability of rolling a 5
and then drawing a 5 from the deck of cards? Write your answer
as a fraction in lowest terms.
Use the formulas and to answer the following question:
22. Suppose on a particular day, the probability (among the
entire population) of getting into a car accident is 0.04, the
probability of being a texter-and-driver is 0.14, and p(car
accident or being a texter-and-driver)=0.15. Find the probability
a person was in a car accident given that they are a texter-and-
driver. Is this higher or lower than the probability among the
general population and why?

5. Remember the formula for expected value is: EV = Outcome1 *
Probability1 + Outcome 2 * Probability2… and so on.
23. You roll a die and win $1 if you get a 2 or 6, lose $2 if you
get a 3, win $5 if you get a 6, and lose $3 if you get a 1. What is
the expected value of this game? If you played the game
repeatedly, would you expect to win money? Why?
24. Suppose you are playing a game with two dice at a casino. If
you roll double ones, you win $1, if you roll double twos, you
win $2. This pattern continues, up to winning $6 for double
sixes. If you roll anything besides doubles, you lose $1. What is
the expected value of the game? Can you expect to win money
by playing this game repeatedly? *Hint: Find the total number
of outcomes of this game first. Only six outcomes win money.
The other outcomes lose money. You’ll find the expected value
with these outcomes. Good luck �
Xiuting Pang
Online English 300
04/29/20
Introduction

6. · It is obvious that no matter which country education has its
own problems. Education is such a complex and important cause
that no country can provide perfect education. Every country is
striving to establish an education mechanism suitable for its
own national conditions. However, the shortcoming and
advantages of the American education system are still worth
explaining. What problems exist in the American education
system, and how to solve them? The main difference between
the education system in the United States and that in most other
countries is that the education system in the United States and
that in most other countries is that education in the United
States is for everyone in the society, not for few. The main
purpose of American education is to develop the talents of
every child, no matter how high or low he is, while instilling a
sense of citizenship in every child. Education in the United
States is mainly provided by the government, controlled and
funed by three levels of government-the federal government,
state government, and local government.
Body
· Education management in the United States is the
responsibility of the state or local government, not the coalition
government. However, the Federal Ministry of Education can
exert a certain degree of influence by controlling the education
fund. In elementary and secondary schools, the curriculum,
funding, teaching and other policies are determined by the local
district committee. School districts are usually separated from
other local affairs based on officials and budgets. Education
standards and standard tests are usually set by the government.
The American education system can be divided into four stages
as a whole, namely Pre-school Education, Elementary
Education, Secondary Education, and higher Education. From
pre-school education, elementary education to secondary
education, all belong to pre-college education, including
Nursery School and Kindergarten, Elementary School, Junior
High School, and High School.

7. · The biggest disadvantage of the American education system is
the unequal educational opportunities. Rich Americans can go
to private schools, but very poor Americans can only go to
public schools. Some schools will provide scholarships but most
Americans cannot afford tuition fees themselves. Another
problem is that public schools are often underfunded. Students
cannot read books because their school does not have a library,
and cannot take physical education classes because students
have no place to exercise and so on. In my opinion, the U.S.
government should pay attention to this issue because if
children have limited educational opportunities, their future
lives will be greatly affected. The advantage is that Americans
have many educational options. School choices include
privated, public, and professional. In addition, many American
schools also provide many extracurricular activities. For
example, sports, book clubs, internships, etc. These
extracurricular activities allow students to make friends or help
them apply for college in the future.
Xiuting Pang
Pang
Online ENGWR 300
04/12/20
Pang
1. What was your main research question?
a. Does the white teachers really have bias against the black
children towards their behaviors in school?
2. What writing/reading/researching strategies and tools did you
use and find helpful? What made them helpful?
a. Resources that I have found in the academic library.
3. Did you find it helpful to see other people's drafts or to meet
with a WAC instructor? Explain.

8. a. Yes, people’s draft helps me with more ideas of how to write
the exploratory essay.
4. Did you run into any difficulty completing this assignment?
If yes, please explain what challenges you faced and what you
did to overcome them.
a. Although this is the first time I’ve written an exploratory
essay, as long as I follow the instructions, it is not that difficult
to write about.
5. What do you like about your final draft? If you had more
time, are there any parts you would change? Why?
a. My final draft is a conclusion explaining how does teacher
brings strong effectiveness of the relationship between white
and black students
6. Anything else you'd like me to know before I read your
paper?
Barriers to Students Success
Historically, the black people in the United States have been
exposed to marginalization, exploitation, discrimination and
even prejudice on the basis of color. Additionally, having been
victims of slavery and all sorts of inhumane acts, most of the
black students have issues with regard to school achievement
and attainment. Different factors have been presented as to why
there exists disparities between the school success between the
white and the black question, with the core question revolving
around the possibility of bias of the white teachers. Therefore,
this research and exploratory essay will involve the analysis of
the question: Does the white teachers really have bias against
the black children towards their behaviors in school? Ideally,
although there has been the formation of movements for the
fighting of liberation of the black people, issues of racism,
inequality and even discrimination seem to be inevitable. The
teacher, in this case, play the central role in the prevalence of
bias, discrimination and the imposition of punishments on the
black students, barring them from desired educational

9. achievement.
Having been in school with black students, some issues are
reality as opposed to the assumed stories made by we, as the
white students. The ideologies presented by the earliest
scholars, for instance, equal but separate by Jim Crow, have
heightened disparities in the school set up. It is a war which
nobody is certain of its end, resulting in the suffering of school.
Although education has been introduced among the black
students, issues such as accessibility, affordability, quality and
the intensity of disciplinary measures imposed by the white
teachers. Additionally, policies such as the zero-tolerance have
also heightened the existence of disparities in the success of the
students, reducing the school attainment. When analyzing the
problem from the contemporary worldview, the teachers are the
core problem in the success of the black students, on the basis
of bias. Some of the studies have indicated that the words and
that statements made by the teachers hurt the black students,
whether done deliberately or even unconsciously.
Although most of us, that the white students, have little
experience of the suffering and the plights of the black people,
historical texts and writing help us familiarize with all these.
Ideally, the suppression of the suffering of black people has
taken a new dimension in the current world. For instance,
instead of having segregation laws, we have unequal
distribution of resources. Bias has been prevalent in the school
set-up, with the teachers playing the big role.
For years, most of the black students have been lagging behind
in terms of academic achievement when compared to their
counterparts, that is the white students. Reports presented by
the National Center for Education in the year 2014 indicate that,
statistically, the graduation rate for the white students was
approximately 83% while the black students were roughly 73%.
On the idea of test scores, the same disparity was realized. In
spite of the fact that there are other factors prompting such
disparity, the key problem has been associated with the biases
of the teachers and the administration at large. Anne Gregory, a

10. psychology professor at Rutgers University ascertains that
disparities have taken a new dimension, which can only be
blamed on the teachers.
In many cases, the differences in terms of treatment of the
students may not be malicious or even intentional. As a result,
it has been realized that some of the disparities are as a result of
cultural misunderstandings, while others have been termed as
implicit bias which is not intentional. Maryland University
Psychologist, Millie Killen has clearly stated that total
elimination of bias is inevitable. What this means is that people
have the role of avoiding acting on their biases. Reading and the
analysis of different resources has enabled me in the
understanding of the intensity of bias in the education system.
For instance, teachers in most cases hardly identify blacks’
students with outstanding academic achievement. For example,
according to the data presented by the study done by Early
Childhood Longitudinal, Sean Nicholson-Crotty together with
other colleagues realized that 54% of the black students were
less likely to receive the recommendation for programs which
are educated- gifted, when compared to the whites. Such
recommendations did not put into consideration aspects such as
the test scores which were standardized (Owens & McLanahan,
2019). On the contrary, in the event whereby the black students
had black teachers then they had high chances of getting
referrals for such programs.
From my own understanding and perception, expectations of the
teachers should be held accountable and responsible for such
disparities. Most of the white teachers do not expect black
students to excel more than the white ones. Additionally, Seth
Gershenson, from a university in America evaluations done by
both white and black teachers on the evaluation of ne black
student, 12% of the white teachers are likely to predict
completion of school by the black student, as well as 30%
prediction of the graduation possibility. When it comes to the
giving of feedback, for instance in essays, most of the white
teachers give more criticism on poorly written work by blacks

11. when compared to whites. This resource is essential for my
research in that it gives a clear guide on the excellence rates of
the white students when compared to the white ones. Moreover,
the low school attainment and performance of the black students
is attributed to biases in marking and the making of referrals,
especially when done by the white teachers.
Racial bias influences not only the teaching but also the
mannerism of discipline imposition on the students, as a result
of misbehavior. Data collected and presented by the department
of Education’s Office of the Civil Rights in the United States
back in 2013 and 2014 indicated that black students in the K-12
level received more suspensions when compared to the whites.
This does not necessarily mean that black students cause most
of the problems as noted by Gregory. Most of the studies done
have indicated that most of the white teachers take advantage of
the socioeconomic status, behaviors self-reported as well as the
reported behavior by other teachers for punishing the black
students. As a result, most of the punishments imposed on the
black students tend to be disproportional. Students suspended
from schools tend to drop out, and become run-ins in the
systems of juvenile justice (Bacher-Hicks, Billings & Deming,
2019). Repetition of this pattern, (that is suspension, dropping
out and juvenile cases) have resulted in the documentation of
various literatures, termed as the “school-to-prison pipeline.”
Reading these reports by researchers enabled me to realize that
most of the disparities and gaps in discipline can be done in a
subtle manner. Research done by psychologists from Stanford
University, that was Jennifer Eberhardt and her colleague Jason
Okonofua discovered that handling of cases of misbehavior by
the teachers is not influenced by the held stereotypes for that
particular group of people. These assertions only applied in the
first infraction, and indication that repeat of such behavior
incorporated the underlying stereotypes. For instance, in the
case of black students, description of troublemakers is used,
making the punishment be extremely harsh as a way of instilling
desired behavior. Implicit bias prompts teachers in making

12. assumptions that misconduct has direct correlation with
misbehavior. Therefore, they say that stereotyping of the blacks
as troublemakers and even violence is borrowed in cases of
misbehavior in schools (Gopalan & Nelson, 2019). On the other
hand, I say that imposition of punishment should be based on
facts, rather than summed up stereotypes and irrational
assumptions.
This article is essential for the study of the issue of bias due to
the presentation of well-researched and factual information.
Based on the ideologies presented by the researchers, there has
been clarity on the relationship between color and the
imposition of discipline in different levels. Despite the
effectiveness of the article in addressing the issues of bias in
discipline measures between the black and white students,
reactions of the students have not been included. For instance,
when black students realize that they are being suspended from
school due to misbehavior which is heightened by their color,
how do they take it? Do they become more violent when they
return to school? Or do they suppress the violent behavior
presumed to be possessed? On the other hand, do the white
students bother about the privileges they enjoy because of
color?
According to reports presented by the researchers in the Negro
Education Journal, higher rates of the suspension of the black
students exists. When these suspension rates are compared to
those of students from other ethnicities and races, cases of
blacks are still the highest. Analysis of the suspension data over
a period of three years was conducted for the explanation of the
school variability percentages on the black students in the
secondary schools in the urban parts. Analysis of the results in
backward hierarchy elimination showed that explanation for the
high percentages of suspension of the white students, the
increment of the school attainment and achievement
discrepancies between the black students and the white ones.
Variables used in the model and the percentages of the school
enrolment of the black students, instructional staff who were

13. blacks as well as the novice of the instructional staff hardly
give the prediction of the suspension possibilities of the black
students (Mitchell, M. M., Armstrong, G., & Armstrong, T.
2020). Therefore, the variations in the suspension rates of the
black students is dependent on unpredictable variables, for
instance, the race of the teacher.
This resource is crucial for my research topic in that it aids in
the explanation of the guidelines dictating suspension variables.
Additionally, I have also noted that suspensions are not prone to
the black students alone, but also includes the white ones as
well. This means that most of the variations are based on
tangible facts, rather than assumptions. Although most of the
black students tend to be more vulnerable to suspensions,
conformity to the set guidelines of the institutions mitigates the
occurrence of such chances. Ideally, variability of these rates of
suspension elaborate as to why there exists some correlation
between the percentages of the suspensions in the different
ethnicities and races in the United States.
Unfortunately, most of the early trainees of the black students
often identity and brand black boys as troublemakers at a very
early age. Walter Gilliam, directing the School of Medicine in
the Yale University, when directing Edward Zigler Center in the
Child Development as well as Social Policy documented the
cases of expulsions in the preschool. In the case of a child,
Walter Gilliam realized that there are three factors that made a
preschool child be more vulnerable in being kicked out of
school. These factors tend to be child-related and include the
following: being black, looking a little bit older when compared
to other classmates as well as being male. Moreover, studies
done by scholars and researchers, for instance, Phillip Atiba
Goff found out that students from the different racial
backgrounds, involved the overestimation of both the age
inclusive of the culpability (Anobile, Guerrini, Burr, Monti, Del
Lucchese & Cicchini, 2019). On the other hand, when
addressing the issue from the implicit bias perception, the
African American boys are not only culpable but also the most

14. dangerous, resulting in the imagination of high possibility of
suspension and expulsion from schools.
Resource is significant in the study in that it aids in
understanding that the marginalization and the stereotyping of
the black male gender starts at early stages. I find it hard to
believe how a preschool teacher can judge the violence or even
the vulnerability of extreme misbehavior at such an early age.
To some extent, I would argue that the teachers ought to be
accountable for such bias. Rationale for my assertion is based
on the fact that, at such an early stage, most of the behavior of
the child is learnt from the surrounding. Therefore, the question
of the role of school in shaping the desired behavior should be
put into consideration.
To conclude, from this exploratory research paper and essay, it
is evident that racial disparities in the schools are heightened by
the teachers. Issues of the magnitude of discipline, the academic
attainment and achievement is highly dependent on the race of
the teacher. As a result, cases of disparities and gaps seem
inevitable between the black and white students. As well, there
is evidence that black students disproportionately face harsh
discipline actions in the school, for instance suspensions or
even in and out of school suspensions. Punitive actions imposed
on the black students result in low academic achievement.
Rationale for this assertion is based on the fact that disciplinary
policies interfere with the time that the student could have spent
engaging in meaningful educational activities.
References
Anobile, G., Guerrini, G., Burr, D. C., Monti, M., Del
Lucchese, B., & Cicchini, G. M. (2019). Spontaneous
perception of numerosity in pre-school children. Proceedings of
the Royal Society B, 286(1906), 20191245.
Arcia, E. (2007). Variability in schools' suspension rates of

15. black students. The Journal of Negro Education, 597-608.
Bacher-Hicks, A., Billings, S. B., & Deming, D. J. (2019). The
School to Prison Pipeline: Long-Run Impacts of School
Suspensions on Adult Crime (No. w26257). National Bureau of
Economic Research.
Gopalan, M., & Nelson, A. A. (2019). Understanding the racial
discipline gap in schools. AERA Open, 5(2),
2332858419844613.
Mitchell, M. M., Armstrong, G., & Armstrong, T. (2020).
Disproportionate school disciplinary responses: An exploration
of prisonization and minority threat hypothesis among black,
Hispanic, and Native American students. Criminal Justice
Policy Review, 31(1), 80-102.
Owens, J., & McLanahan, S. S. (2019). Unpacking the drivers
of racial disparities in school suspension and expulsion. Social
Forces.
Teague, J. (2019). Middle School Teachers’ Perceptions of
Factors that Contribute to the Discipline of African-American
and Impoverished Males in Urban Schools: A Qualitative Case
Study (Doctoral dissertation, Northcentral University).
Essay 3: Addressing Barriers to Student Success
Background and Task:
In the previous unit, we explored various contemporary
issues/barriers faced by students within the US educational
system (K-college). Through an exploratory research paper, you
focused on a specific student population and/or factor that
negatively impact student success and reported on various
perspectives on the topic. While your purpose in the research

16. paper was to develop and demonstrate your research skills and
awareness of the complexity of your chosen research topic, your
purpose for this assignment is to present an argument and
convince readers about how to best address a key problem you
identified in your research.
Your task is to write a 1250-word persuasive essay, in which
you present your position on how to best address a key issue
that negatively impact student success — based on your
research. The idea is for you to build on the writing/reading
skills and knowledge you gained from your exploratory
research, so please focus on the same topic.
Audience:
Imagine other college students, faculty, and staff who do not
have much background in this topic and whom you must
convince about your claim/opinion.
Your goal is to write an essay that...
· has a clear and well-supported claim (your thesis) and a title
that reflects this
· integrates ideas from 3-4 sources--one of which must be an
academic/scholarly source (these may be the same sources you
used for your annotated bib or exploratory research). Note: the
reasons and evidence you use to support your argument must
come primarily from outside sources versus personal experience
· helps readers understand the complexity of the issue (this
means incorporating multiple perspectives)
· refutes counterarguments or opposing views (when applicable)
· employs rhetorical strategies/persuasive devices (ethos,
pathos, logos, kairos)
· is organized in a logical and coherent fashion
· uses “quotation sandwiches” and adhere to the MLA citation
and formatting guidelines.
· meet all other requirements and the minimum standards listed
on the rubric on Canvas

17. Specifics:
Length: 1250 words (about 5 pages) -- not counting the Works
Cited page
Formatting: double-spaced, 12 pt font (Times New Roman),
following MLA guidelines
Sources: 3-4 sources total, one of which must be an
academic/scholarly source (you may use the
same sources from your exploratory research paper, if
applicable.
Final Draft DUE : Saturday May 2nd at 11:59pm via Canvas