Graded Discussion: The Monty Hall Problem
Requirements:
A minimum of two posts is required.
You must give a detailed explanation for each part in your first post to get full credit. Use complete sentences, correct punctuation, and correct grammar.
You will be able to see other students' posts once you post your own solution. Review their responses to determine if they agree with your own.
For your second post, reply to a classmate's post.
Complete required posts by the posted deadline.

Part 1: Prepare
Read this scenario:
You're on the game show "Let's Make A Deal" looking at 3 doors. Behind one is a brand-new car. Behind the others are goats! You get to choose one door: if it's the car, you win! You choose Door #1. But before he unveils its contents, Monty opens Door #2 and reveals a goat. You may have picked the right door! Monty asks if you'd like to make a deal. If you want, you can switch to Door #3. What would switching do: improve your odds, worsen your odds, or leave them the same? Answer this question on a piece of paper BEFORE viewing the following video.
Watch the video:
https://youtu.be/2Kgud9QcZs4
Read the explanation:

When you choose Door #1, your odds of winning are clearly 1/3. Therefore, the odds that the prize is behind Door #2 or Door #3 is 2/3. When Monty reveals that there is nothing behind Door #2, it doesn't change the original probabilities. There is still a 2/3 chance that the prize is behind door two or three. (Knowing the contents of door two doesn't change the odds once you've started playing.) Therefore, door three now has a 2/3 odds of winning.
Part 2: First Post

Title Your Post: Students name Monty Hall Problem Post
Answer each question:
1) Before you watched the video, did you think you should stay or switch. (4 points)
2) After you watched the video, did you change you mind? Explain your reasoning. (4 points)
Part 3: Second and Third Posts
Second and Third Posts (2 points): Read and reply substantively to two classmates' posts.

Graded Discussion: Misleading Graphs
Requirements:
A minimum of one post is required.
You must give a detailed solution to each question in your post to get full credit.
It is not enough to just give the final answer.
You must show steps or explain your reasoning.
If it is easier, you can write your solution out on paper, take a picture, and upload it to the discussion as a pdf file. The pdf file type is the only file type that will be accepted.
You will be able to see other students' posts once you post your own solution.
Review their responses to determine if they agree with your own.

You are not required to make a second post, but you can reply to your own post with corrections.   Don't worry!  You will not lose points for an incorrect answer in your first post as long as you make a reasonable effort on the first post and post a reply with the correct answer in your second post.  
Complete required posts by the posted deadline.

Part 1: Prepare

Read this article about the way graphs can be misleading. https://www.statisticshowto.com/probability-and-statistics/descriptive-statistics/misleading-graphs/

Source of data: https://www.bls.gov/careeroutlook/2020/data-on-display/education-pays.htm

[2 pts] What is the ratio of the median weekly earnings of the holder of a high school diploma only to the median weekly earnings of the holder of a bachelor's degree?
[2 pts] What is the ratio of the area of the red rectangle to the area of the blue rectangle in graph A? (The scale on the horizontal axis is 1 unit per grid mark.)
[2 pts] What is the ratio of the area of the red square to the area of the blue square in graph B? (The scale on the horizontal axis is 1 unit per grid mark.)
[2 pts] What is the ratio of the volume of the red cube to the volume of the blue cube in graph C? (The scale on the horizontal axis is 1 unit per grid mark and the bases of the prisms are squares.)
[2 pts] Explain which graph is the most misleading and give a mathematical justification for your answer.

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