This project consists of 5 questions/activities. You can either print this document (not including this
page), complete it by hand, scan it, and email that scanned file to me OR you can complete the
document in Microsoft Word. If you choose to complete the project using MS Word, you must make
sure that the formatting stays relatively similar to the original formatting.
When each part of the project is complete, please e-mail cindy.langley (in eSchoolware) or
cindy.langley@sc.provostacademy.com. Please be sure to include your name and which project you are
submitting. For example, Cindy Langley MT4 Part 2 Project 1.
Please contact me with any questions or concerns.
eSchoolware: cindy.langley
Provost email: cindy.langley@sc.provostacademy.com
Cell: 803.465.7471
Whether you are watching the game show Wheel of Fortune of playing Hangman with a friend, it helps
to know which letters have the highest probability of use in words. During this project you will conduct
an experiment and collect statistical data to discover which letters are most commonly used in written
English language.
Probability, or the likelihood that a specific event will occur, can be determined theoretically or
experimentally. Theoretical probability is a ratio that compares the number of specific outcomes to the
total number of outcomes possible. For example, to calculate the probability of rolling the number 2 on
a number cube, divide 1 (the number of specific outcomes that are a 2) by 6 (the number of total
possible outcomes) to determine the theoretical probability of 1/6 or about 16.7%. Theoretical
probability can only be determined by mathematical calculation.
Experimental probability is based on performing an actual experiment to collect data. To determine the
experimental probability simply divide the number of times that an actual event occurs by the number
of times that the experiment is done. For instance, if you flip a coin and it lands on tails 27 out of 50
times, then the experimental probability of getting tails is 27/50 or 54%. This is higher than the
theoretical probability of ½ or 50%.
1) If we took the 26 letters of the alphabet and placed them in a hat and then asked you to choose
one without looking, the theoretical probability of choosing each letter would be 1 out of 26 or
about 3.8%. However, if we choose a letter at random out of a book or other written material,
does each letter still have an equal probability of being chosen? Explain.
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2) To find the probability of choosing any letter in the alphabet (at random) out of a book or other
written source, would you use theoretical or experimental probability? Why?
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3) To find the experimental probability of each letter in the alphabet being used, you will collect
250 letters randomly by selecting a small reading passage and then recording your data on the
following page. Use 250 consecutive letters. Do not skip around on the page.
Before beginning, predict what you thing the top five most-used letters will be.
1.
2.
3.
4.
5.
4) Using the 250 letters from your randomly selected reading passage, fill in the individual data in
the chart below.
LETTER
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
Number in Sample
% of 250 Letters
Letter Rank
Please include a copy of the sample text you used below:
Sample Text
5) Based on your experiment, if you were a contestant on the game of Wheel of Fortune playing in
the bonus round, what 3 consonants and 1 vowel would you choose in addition to the ones you
are given to start (R, S, T, L, N and E). Why?
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Grading Rubric
Student Name:
CATEGORY
Mathematical
Concepts
________________________________________
4
Explanation
shows
complete
understanding
of the
mathematical
concepts used
to solve the
problem(s).
Uses complex
and refined
mathematical
reasoning.
3
Explanation
shows
substantial
understanding
of the
mathematical
concepts used
to solve the
problem(s).
Uses effective
mathematical
reasoning
2
Explanation shows
some
understanding of
the mathematical
concepts needed
to solve the
problem(s).
1
Explanation shows
very limited
understanding of
the underlying
concepts needed
to solve the
problem(s) OR is
not written.
Some evidence of
mathematical
reasoning.
Little evidence of
mathematical
reasoning.
Explanation
Explanation is
detailed and
clear.
Explanation is
clear.
Explanation is a
little difficult to
understand, but
includes critical
components.
Completion
All problems
are
completed.
All but one of
the problems
are completed.
All but two of the
problems are
completed.
Explanation is
difficult to
understand and is
missing several
components OR
was not included.
Several of the
problems are not
completed.
Mathematical
Reasoning