# counting techniques and introduction to probability

MATH125: Unit 4 Submission Assignment Answer Form

Counting Techniques and Introduction to Probability

ALL questions below must be answered. Show ALL step-by-step calculation. Upload this modified Answer Form to the intellipath Unit 4 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 & Permutations

1. Differentiate between permutations and combinations. How are they different? What is the formula for each? (15 points)

How are they different?

(5 pts)

?

Permutation Formula

(5 pts)

?

Combination Formula

(5 pts)

?

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)

(1 pt)

?

(Or a Sample)

(1 pt)

?

(1 pt)

?

a. Determine the number of different license plates that can be created using this 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 all alphanumeric characters only once.

Is   this a permutation or combination? Why?

(2   pts)

?

What   formula from #1 above will you use to solve the problem?

(1   pt)

?

Solution:

(4   pts)

?

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 pt)

?

(Select a number from 2 to 5)

What are the characters at the beginning?

(1 pt)

?

(4 pts)

?

How many license plates have been   eliminated?

(4 pts)

?

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 with three different age groups. How many different ways can you organize teams of ten for each age group? (15 points)

Are these a permutation or combination? Why?

(2 pt)

?

What formula from #1 above will you use   to solve the problem?

(1 pt)

?

How many students signed up for soccer?

(1 pt)

?

(Select a multiple of 10, from 30 to 100)

How many kids signed up for “Little Tykes”   under the age of seven?

(1 pt)

?

(Select a multiple of 10, of at least 20)

How many kids signed up for “Big Kids”   between 8 and 12?

(1 pt)

?

(Select a multiple of 10, of at least 20)

How many kids signed up for “Teens”   between 13 and 18?

(1 pt)

?

(Select a multiple of 10, of at least 20)

How many different ways can you create   teams of ten for the “Little Tykes” grade level?

(2 pts)

?

If age levels did not matter, how many   different ways can you create teams of ten?

(2 pts)

?

Part B: Probabilities and Odds

4. For this set of exercises, you will need one standard six sided dice. If you don’t have one, you can use virtual dice: https://www.random.org/dice/,  (40 points total)

a. First, let’s differentiate between “odds” and “probability”.

How   are odds and probability different?

(2   pts)

?

What   is the “odds of in favor” ratio?

(3   pts)

?

What   is the “probability of an event” ratio?
(3 pts)

?

What   are the odds of rolling a three? (Simplify all fraction answers.)
(2 pts)

?

What   is the theoretical probability of rolling a three? (Simplify all fraction   answers.)
(2 pts)

?

b. Please 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 pts)

?

Next, given the “Likelihood Scale” table above, what term best describes your answer?

Likelihood Scale

Term

(2 pts)

?

a. What if someone challenged you to NEVER roll a 3? If you were to roll the dice 18 times, what would be the empirical probability of never getting a three?

Percent Probability

Solution:

(Rounded to the nearest whole percent.)

(2 pts)

?

b. 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 pts)

?

Likelihood Scale Term

(2 pts)

?

c. What if someone challenged you to NEVER roll a 3? If you were to roll the dice 18 times, what would be the empirical probability of never getting a three?

Percent Probability

Solution:

(Rounded to the nearest whole percent.)

(2 pts)

?

What   do you notice about the answers for parts c. and d. above?

(2 pts)

?

d. Roll the dice 18 times and keep track of what is rolled in the table below. (2 points)

Roll   #

Dice

Roll   #

Dice

Roll   #

Dice

Roll 1

?

Roll 7

?

Roll 13

?

Roll 2

?

Roll 8

?

Roll 14

?

Roll 3

?

Roll 9

?

Roll 15

?

Roll 4

?

Roll 10

?

Roll 16

?

Roll 5

?

Roll 11

?

Roll 17

?

Roll 6

?

Roll 12

?

Roll 18

?

e. Based on your dice 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 pts)

?

Likelihood Scale Term

(2 pts)

?

In regards to the “Likelihood   Scale” terms for each, how did this differ from both the theoretical   and empirical probability?

(2 pts)

?

Pages (550 words)
Approximate price: -

Why Work with Us

Top Quality and Well-Researched Papers

We always make sure that writers follow all your instructions precisely. You can choose your academic level: high school, college/university or professional, and we will assign a writer who has a respective degree.

We have a team of professional writers with experience in academic and business writing. Many are native speakers and able to perform any task for which you need help.

Free Unlimited Revisions

If you think we missed something, send your order for a free revision. You have 10 days to submit the order for review after you have received the final document. You can do this yourself after logging into your personal account or by contacting our support.

Prompt Delivery and 100% Money-Back-Guarantee

All papers are always delivered on time. In case we need more time to master your paper, we may contact you regarding the deadline extension. In case you cannot provide us with more time, a 100% refund is guaranteed.

Original & Confidential

We use several writing tools checks to ensure that all documents you receive are free from plagiarism. Our editors carefully review all quotations in the text. We also promise maximum confidentiality in all of our services.

Our support agents are available 24 hours a day 7 days a week and committed to providing you with the best customer experience. Get in touch whenever you need any assistance.

Try it now!

## Calculate the price of your order

Total price:
\$0.00

How it works?

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Our Services

No need to work on your paper at night. Sleep tight, we will cover your back. We offer all kinds of writing services.

## Essay Writing Service

No matter what kind of academic paper you need and how urgent you need it, you are welcome to choose your academic level and the type of your paper at an affordable price. We take care of all your paper needs and give a 24/7 customer care support system.