MATH125 AIU Counting Techniques and Probability Paper All questions have to be answered and show all step by step calculations. Text book used is General C

MATH125 AIU Counting Techniques and Probability Paper All questions have to be answered and show all step by step calculations. Text book used is General College Math by editorial board, Words of Wisdom. NAME:
MATH125: Unit 8 Submission Assignment Answer Form
Counting Techniques
ALL questions below must be answered. Show ALL step-by-step calculation. Upload this modified
Answer Form to the intellipath Unit 8 Submission lesson. Make sure you submit your work in a modified
MS Word document; handwritten work will not be accepted. If you need assistance, please contact your
course instructor.
Part A: Combinations and Permutations
1. Differentiate between permutations and combinations. How are they different? What is the
formula for each? (15 points total for Question 1)
How are they different?
(5 points)
?
Permutation Formula
(5 points)
?
Combination Formula
(5 points)
?
2. Each state has a standard format for license plates that includes a set number of alphanumeric
characters. For this assignment, you can insert a picture of your state’s non-personalized license
plate or provide a sample of the format in text. (20 points total for Question 2)
Your State’s Name
(1 point)
Picture of a License Plate
from Your State
(or a Sample)
(1 point)
?
?
Describe the Character
Rule for Your State’s
Non-personalized
License Plates
(1 point)
?
a. Determine the number of different license plates that can be created using the
following format. Assume that a license plate consists of seven alphanumeric characters
using numbers (0–9) and capital letters (A–Z). Find how many unique license plates can
be printed using any of the 36 alphanumeric characters without duplication in each of
the seven alphanumeric characters, i.e., no alphanumeric character appears more than
once in any license plate. (This question is NOT related to your state’s license plates in
the initial 3 parts above).
Is this a permutation or
combination? Why?
(2 points)
What formula from
Question 1 will you use
to solve the problem?
(1 point)
Number of unique
license plates that can be
printed:
(2 points)
?
?
?
Show your work here (2 points):
b. You and a friend are witnesses of a car accident in your state. But you can only
remember a few of the first alphanumeric characters on the license plate.
How many alphanumeric
characters do you
remember?
(1 point)
?
(Select a number from 2 to 5)
What are the characters
at the beginning?
(1 point)
?
How many license plates
start with these
alphanumeric
characters?
(2 points)
?
Show your work here (2 points):
How many license plates
have been eliminated?
(2 points)
?
Show your work (2 points):
3. Your community has asked you to help the YMCA sports director organize a season of sports.
You need to put together the teams. For the soccer teams, athletes signed up for one of three
different age groups (Little Tykes, Big Kids, and Teens). (15 points total for Question 3)
Is this a permutation or
combination? Why?
(2 points)
?
What formula from
Question 1 will you use
to solve the problem?
(1 point)
?
How many kids signed
up for “Little Tykes”?
(1 point)
How many kids signed
up for “Big Kids”?
(1 point)
?
(Select a multiple of 10, of at least 20)
?
(Select a multiple of 10, of at least 20)
How many kids signed
up for Teens?
(1 point)
How many total
students signed up for
soccer?
(1 point)
?
(Select a multiple of 10, of at least 20)
?
(enter total form the three groups above)
Use the formula and values, from question above, to answer the following:
How many different
ways can you create
teams of 10 for the
“Little Tykes” grade
level?
(2 points)
?
Show your work here: (2 points)
If age levels did not
matter, how many
different ways can you
create teams of 10 from
?
the total number of
soccer players?
(2 points)
Show your work here: (2 points)
Part B: Probabilities and Odds
4. For this set of exercises, you will need a single standard six-sided die. If you do not have one,
you can use a virtual die: https://www.random.org/dice/ (40 points total for Question 4)
a. First, differentiate between odds and probability.
How are odds
and probability
different?
(2 points)
What is the
odds in favor
ratio?
(3 points)
What is the
probability of
an event ratio?
(3 points)
?
?
?
?
What are the odds of
rolling a three (use the
proper ratio from above)?
Simplify all fraction
answers.
(2 points)
What is the theoretical
probability of rolling a
three (use the proper
ratio from above)?
Simplify all fraction
answers.
(2 points)
?
b. Reflect on the previous question’s answer outcome. First, convert the fraction to a
percent.
Percent Probability
Theoretical Probability
(Rounded to the nearest
whole percent.)
(2 points)
?
Next, use the likelihood scale table above to select the term that best describes your answer.
Likelihood Scale
Term
(2 points)
?
c. What if someone challenged you to never roll a 3? If you were to roll your single sixsided die 18 times, what would be the empirical probability of never getting a three?
Also, list the likelihood scale term from the table above.
Percent Probability
Solution
(Rounded to the
Nearest Whole Percent)
(2 points)
Likelihood Scale Term
(2 points)
?
?
Show your work here: (2 points)
d. After 18 rolls, what would be the empirical probability of getting a three on at least one
of those rolls? Also, list the likelihood scale term from the table above.
Percent Probability
Empirical Probability
(Rounded to the
Nearest Whole Percent)
(2 points)
Likelihood Scale Term
(2 points)
?
?
Show your work: (2 points)
What do you notice
about the answers for
parts c and d above?
(2 points)
?
e. Roll the die 18 times and keep track of what is rolled in the table below. Remember, if
you do not have one, you can use virtual dice: https://www.random.org/dice/ (2 points)
Roll #
Roll 1
Roll 2
Roll 3
Roll 4
Roll 5
Roll 6
f.
Dice
Roll #
Dice
Roll #
Dice
?
Roll 7
?
Roll 13
?
?
Roll 8
?
Roll 14
?
?
Roll 9
?
Roll 15
?
?
Roll 10
?
Roll 16
?
?
Roll 11
?
Roll 17
?
?
Roll 12
?
Roll 18
?
Based on your die rolls, what is the experimental probability of rolling a three, out of 18
rolls? Also, list the likelihood scale term from the table above.
Percent Probability
Experimental Probability
(Rounded to the Nearest
Whole Percent)
(2 points)
Likelihood Scale Term
(2 points)
?
?
Show your work here: (2 points)
With regard to the
likelihood scale terms
for each, how did this
differ from both the
theoretical and empirical
probabilities?
(2 points)
?

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