Module 14 Homework 1 – Introduction to Inference (2 of 4)

Learning Goal: I’m working on a statistics question and need an explanation and answer to help me learn.

Progress Check

Use this activity to explore how probability is used in statistical inference.

Context

You are studying with one of your classmates who is acing this class. She displays the following picture.

A deck of 52 playing cards, face up. There are 26 black cards, 26 red cards. There are 4 suits (clubs, spaces, hearts, and diamonds) with 13 cards in each suit. There 12 "face cards."

Then she pulls out a new deck of cards. She removes the plastic wrap from the deck of new cards, opens the box, and pulls out the cards. She removes the jokers and any other cards not displayed in the picture above. Then she starts shuffling the cards – which is difficult because the cards are brand new and slippery. She continues to shuffle and reshuffle until you agree that the deck is well-shuffled. Then she sets the deck down.

To verify that you know how to calculate various probabilities for a randomly drawn card, she asks the following questions which you answer correctly.

  • If I randomly select a card, what is the probability of drawing a red card?
    YOUR ANSWER: 26/52 = 0.5 or 50%
  • If I randomly select a card, what is the probability of drawing a 9?
    YOUR ANSWER: 4/52 ≈ 0.0769 or 7.69%

  • If I randomly select a sample of two cards, what is the probability that both cards are red?
    YOUR ANSWER: (26/52)(25/51) ≈ 0.2451 or 24.51%

  • In the above calculation you multiplied, (26/52)(25/51). Why?
    YOUR ANSWER: Randomly selecting a sample of two cards means we draw two cards – one at a time without replacement. So a random sample of two red cards means the first card is red and the second card is red. When we randomly select the first card, the probability we draw a red card is 26 red cards out of 52 total cards, or 26/52. We set that first red card aside. So, when we randomly select the second card, there are only 25 red cards out of a total of 51 cards, so the probability we get a red card is 25/51. We need to calculate the probability that the first card is red AND the second card is red. So we multiply the two fractions together, (26/52)(25/51).

Then your classmate says, “O.K. Let’s make a little bet. If you draw a black card, I will help you with all remaining homework in this class.” If not, you must wash and wax my car for me. Since she opened a brand new deck of cards right in front of you and you verified they were well-shuffled, you know the probability of drawing a black card is 0.5 or 50%, so you agree to the bet.

She picks up the deck of cards, fans them out (face down of course), and asks you to randomly select a card. You select a card and turn it over. It’s red – not black.

You set the card aside and ask to try again. She reluctantly agrees and warns that if you lose, you will have to wash and wax her car twice. But if you win, you will not have to wash and wax her car, and she will help you with your homework as promised. You draw another card. It’s red – not black.

You set the card on top of the previously drawn red card and ask to try a third time. Again, she reluctantly agrees, and you draw another card. It’s red – not black. You must now wash and wax her car three times. You decide to quickly calculate the probability of randomly selecting a sample of three red cards.

2652⋅2551⋅2450≈0.1176 or 11.76%

You set the card on top of the previously drawn red cards and think, “The next card has to be black.” You ask to try a fourth time. Again, she reluctantly agrees, and you draw another card. It’s red – not black. You now have a random sample of 4 red cards, and you must wash and wax her car four times.

You set the card on the stack of previously drawn red cards, and ask to try again. Once again, she reluctantly agrees, and you draw another card.

Prompt

  1. What is the probability of drawing a random sample of 4 red cards (write the probability as a decimal and a percentage)? Would you consider the random sample of 4 red cards unusual? Why or why not?
  2. What is the probability of drawing a random sample of 5 red cards (write the probability as a decimal and a percentage)? Would you consider the random sample of 5 red cards unusual? Why or why not?
  3. When your classmate began shuffling the deck of cards, what obvious assumption did you believe was true? If you draw a random sample of 5 red cards from the deck, should you reject that assumption? Why or why not?
  4. Based on your responses to the previous question, what will you infer about the deck of cards?

Module 14 Discussion Board

Use the Module 14 discussion board (opens in a new tab) to ask questions or provide feedback about the problems in any Module 14 activity – including this peer-reviewed assignment.

Review Feedback

  • Peer feedback should be available before final drafts are due.
  • Instructor feedback is only available after an assignment is graded.
  • Use these directions (opens in a new tab) to learn how to review feedback.

Click the “Next” or > button to continue.

Content by Cuyamaca College math faculty and inspired by Dr. Roxy Peck.

Rubric

Peer Review (FD Optional)

Peer Review (FD Optional)
Criteria Ratings Pts
This criterion is linked to a Learning OutcomeFirst Attempt
5 ptsFull Marks

A first attempt was made on this assignment

 0 ptsNo Marks
5 pts
This criterion is linked to a Learning OutcomeAnswering the Prompt
3 ptsFull Credit

All parts of the “Prompt” are addressed, and the responses demonstrate attainment of the learning objectives in the “Progress Check” section of the assignment. The answers are mostly correct. The writing/work is clear. The explanation/work is reasonable, well-organized, and easy to follow.

 1.5 ptsPartial Credit

One or more parts of the “Prompt” are not addressed or are incorrect. Or, answers do not demonstrate attainment of the learning objectives in the “Progress Check” section of the assignment. Or, answers are correct, but the writing/work is unclear, incorrect, or difficult to follow.

 0 ptsNo Marks

The “Prompt” is not addressed or the work is incorrect or missing. Or, the first draft was not a good-faith effort.
3 pts
This criterion is linked to a Learning OutcomePeer Review
2 ptsFull Credit

You completed the assigned peer review. The points you assigned in the rubric for the “Addressing the Prompt” criterion are appropriate. You used the “Add a Comment:” field to submit your assignment comments. Your assignment comments relate the score you assigned in the “Addressing the Prompt” criterion of the rubric to how your peer addressed the learning objectives when responding to the “Prompt.” (Note: the learning objectives are listed in the “Progress Check” section of the assignment.) If you awarded full credit for the “Addressing the Prompt” criterion in the rubric, your comments contextually and specifically explain what your peer did to demonstrate attainment of the relevant learning objectives. If you deducted points for the “Addressing the Prompt” criterion, you clearly explained what your peer can do better to demonstrate attainment of the relevant learning objectives.

 1 ptsPartial Credit

You committed a good-faith effort to provide a high-quality peer review, but necessary instructive comments are missing. Or, you provided appropriate instructive comments but did not complete the rubric.

 0 ptsNo Marks

No peer review provided or the comments are not instructive. Or, you did not commit a good-faith effort on your first draft.
2 pts
Total Points: 10
Calculate your paper price
Pages (550 words)
Approximate price: -

Why Choose Us

Quality Papers

We value our clients. For this reason, we ensure that each paper is written carefully as per the instructions provided by the client. Our editing team also checks all the papers to ensure that they have been completed as per the expectations.

Professional Academic Writers

Over the years, our Acme Homework has managed to secure the most qualified, reliable and experienced team of writers. The company has also ensured continued training and development of the team members to ensure that it keep up with the rising Academic Trends.

Affordable Prices

Our prices are fairly priced in such a way that ensures affordability. Additionally, you can get a free price quotation by clicking on the "Place Order" button.

On-Time delivery

We pay strict attention on deadlines. For this reason, we ensure that all papers are submitted earlier, even before the deadline indicated by the customer. For this reason, the client can go through the work and review everything.

100% Originality

At Buy An Essay, all papers are plagiarism-free as they are written from scratch. We have taken strict measures to ensure that there is no similarity on all papers and that citations are included as per the standards set.

Customer Support 24/7

Our support team is readily available to provide any guidance/help on our platform at any time of the day/night. Feel free to contact us via the Chat window or support email: support@acmehomework.com.

Try it now!

Calculate the price of your order

We'll send you the first draft for approval by at
Total price:
$0.00

How it works?

Follow these simple steps to get your paper done

Place your order

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

Proceed with the payment

Choose the payment system that suits you most.

Receive the final file

Once your paper is ready, we will email it to you.

Our Services

Buy An Essay has stood as the world’s leading custom essay writing services providers. Once you enter all the details in the order form under the place order button, the rest is up to us.

Essays

Essay Writing Services

At Buy An Essay, we prioritize on all aspects that bring about a good grade such as impeccable grammar, proper structure, zero-plagiarism and conformance to guidelines. Our experienced team of writers will help you completed your essays and other assignments.

Admissions

Admission and Business Papers

Be assured that you’ll definitely get accepted to the Master’s level program at any university once you enter all the details in the order form. We won’t leave you here; we will also help you secure a good position in your aspired workplace by creating an outstanding resume or portfolio once you place an order.

Editing

Editing and Proofreading

Our skilled editing and writing team will help you restructure you paper, paraphrase, correct grammar and replace plagiarized sections on your paper just on time. The service is geared toward eliminating any mistakes and rather enhancing better quality.

Coursework

Technical papers

We have writers in almost all fields including the most technical fields. You don’t have to worry about the complexity of your paper. Simply enter as much details as possible in the place order section.

See all services