Unit 06

Unit 6:
Understanding Probability and Chance

Unit 6: Assignment #1 (due before 11:59 pm Central on FRI JUL 5):

In this Unit, you will learn about probability and chance. Let’s start, in this first Assignment, by learning why we can’t trust our intuitions about probability.
1. Watch Professor Gernsbacher’s lecture video, “The Fallibility of our Intuitions about Probabilities.” [A transcript of the lecture video is available here.]
2. While watching the lecture video, be sure to play the Truck Driver vs Professor game. Take either a screenshot or a photo of the page on which you categorized the ten men’s names.
Go to the Unit 6: Assignment #1 Discussion Board and make a new Discussion Board post, of at least 200 words, in which you do the following:
1. First, identify the four Cognitive Biases and give a one-sentence description of each, in your own words.
2. Second, discuss which Cognitive Bias you find the most compelling and provide one more example (NOT an example from the lecture video) of how that Cognitive Bias causes us to disregard base-rate probabilities in favor of our fallible intuitions.
3. Third, embed in your Discussion Board post either a partial screenshot or a photo of the page on which you categorized the men’s names who live in the fictional town.
  - Remember to embed and size your photo using the procedures you learned from the Course How To.
  - NOTE: The Canvas Discussion Board cannot embed either .HEIC or .tiff/.tif images. Therefore, before trying to embed a .HEIC or .tiff/.tif image, you must save the image as a .jpg, .jpeg., or .png image.

Unit 6: Assignment #2 (due before 11:59 pm Central on FRI JUL 5):

In this assignment, you will learn about empirical probability and how it differs from base-rate probability.
1. First, read Carr’s (2017) article, “What Is … Probability in Statistics?”
  - Make sure you understand what P(E) means.
  - Make sure you understand that probabilities are calculated as proportions (e.g., 0.000, .500, and 1.000), although we often talk about them as percentages (e.g., 50% chance).
2. Second, read Khan Academy’s (no date) article, “Probability: The Basics.”
  - Make sure you understand that calculating base-rate probabilities is a lot like computing relative frequency.
To calculate base-rate probability using items in your life:
1. Find a type of item in your current home that you have TEN of and that you can categorize into FOUR categories, for example:
  - Ten pieces of candy that you can categorize into four categories based on color (e.g., red candies, blue candies, green candies, yellow candies) OR that you can categorize into four categories based on candy type (Skittles, M&Ms, Reese’s Pieces, Sour Patch Kids), OR that you can categorize into four categories based on another feature.
  - Ten pieces of cutlery (e.g., silverware) that you can categorize into four categories based on shape (e.g., knives, forks, teaspoons, tablespoons) OR based on use (e.g., everyday, formal, plastic, compostable), OR based on another feature.
  - Ten socks (or other small clothing items) that you can categorize into four categories based on color OR based on style OR based on another feature.
  - Ten pens or pencils that you can categorize into four categories based on color OR based on size OR based on another feature.
  - Ten golf balls that you can categorize into four categories based on color OR based on brand OR based on another feature.
  - Ten hair scrunchies or hair ties that you can categorize into four categories based on color OR based on style OR based on preference OR based on another feature.
  - Ten Lego bricks (or other small toys) that you can categorize into four categories based on color OR based on shape OR based on another feature.
2. NOTE: You only need to categorize your TEN items into one set of FOUR categories (e.g., if you choose pieces of candy, you only need to categorize your candy into color; you don’t need to also categorize your pieces of candy into color AND into candy type AND into another category).
3. Your ten items must be able to fit in a box, bag, basket, or the like because you will need to select your items out of that box, bag, basket, or the like (without looking) later in this assignment.
4. After gathering your ten items, take a photo that shows all ten of your items. Name the image file YourLastName_PSY-210_Unit06_Photo_TenItems.xxx (where xxx is the file type, for example, .jpg, .png, .jpeg, and the like).
  - NOTE: As you learned from the Course How To, the Canvas Discussion Board cannot embed either .HEIC or .tiff/.tif images. Therefore, before trying to embed a .HEIC or .tiff/.tif image, you must save the image as a .jpg, .jpeg., or .png image.
5. Next, using your data management platform, create a Base-Rate Frequency Distribution Table.
  - First, open a new (blank) spreadsheet in your data management system.
  - Second, create a Column Header for your items, for example, Umbrellas (by type), and enter the category names of your TEN items under this Column Header.
  - Third, create a Column Header “Categories” and enter your FOUR category names (e.g., Golf, Foldable, Parasol, Beach) under this Column Header.
  - Fourth, calculate the Absolute Frequency and Relative Frequency of each category.
  - Fifth, remember to adhere to good scientific practice by always using three decimal places for Relative Frequency (and for any other time we use decimals).
  - Sixth, calculate a total for your Absolute Frequency and Relative Frequency columns.
  - Fifth, remember again to adhere to good scientific practice by always using three decimal places for Total Relative Frequency (and for any other time we use decimals).
  - Your Base-Rate Frequency Distribution Table should look like this.
To learn what empirical (or observed) probability is, how empirical probability differs from base-rate probability, and how we calculate empirical probability, read Poldrack’s (2020) Chapter 6, “Probability: Empirical Frequency.”
1. Make sure you understand what empirical (or observed) probability is.
2. Make sure to understand how empirical probability differs from base-rate probability.
3. Make sure you understand what the Law of Large Numbers is.
To calculate empirical probability, using the items in your life:
1. First, place all ten of your items in a box, bag, basket or the like.
2. Second, without looking, select one of your items out of the box, bag, basket.
3. Third, write down the category name of the item you selected (e.g., teaspoon).
4. Fourth, replace the item you selected back into the box, bag, basket.
5. Fifth, mix up the items in the box, bag, basket.
6. Sixth, repeat this process — Select, Write Down, Replace, and Mix — FOUR more times (which means you will have data from a total of five trials).
7. Seventh, in your spreadsheet, create another Frequency Distribution Table using the data you collected in your five trials.
  - Create a Column Header for your selected items that is named your item type (e.g., Umbrellas), followed by the word Selected, followed by a dash, and a 5 (e.g., Umbrellas Selected – 5).
  - Under the Column Header you just created, enter the results of your five trials by listing the category name of each of the five items you selected.
  - Create a Column Header “Categories” and enter your four category names under this Column Header.
  - Calculate the Empirical Absolute Frequency and the Empirical Relative Frequency of each category.
  - Remember to adhere to good scientific practice by always using three decimal places for Empirical Relative Frequency (and for any other time we use decimals).
  - Calculate a total for your Empirical Absolute Frequency and Empirical Relative Frequency columns
  - Remember again to adhere to good scientific practice by always using three decimal places for Total Empirical Relative Frequency (and for any other time we use decimals).
  - Your Empirical – Five Trials – Frequency Distribution Table should look like this.
Repeat the entire process of step d above, only this time rather than conducting only five trials, conduct twenty-five (25) trials.
1. Therefore, instead of computing Empirical Probabilities after five trials, you will compute Empirical Probabilities after twenty-five trials.
2. Your Empirical – Twenty-Five Trials – Frequency Distribution Table should look like this.
Take ONE screenshot that contains ALL three of your three frequency distribution tables.
1. Meaning: Take one partial screenshot that contains all three of your frequency tables in ONE screenshot.
2. Your partial screenshot should include only your three Frequency Distribution Tables NOT your entire screen.
3. Save the screenshot and name it YourLastName_PSY-210_Unit06_Screenshot_Probability.xxx (where xxx is the file type, for example, .jpg, .png, .jpeg, and the like)
After creating your two Frequency Distribution Tables, examine your findings.
1. How closely did your empirical probabilities match your base-rate probabilities when you conducted only five trials?
2. How closely did your empirical probabilities match your base-rate probabilities when you conducted twenty-five trials?
3. If your empirical probabilities better matched your base-rate probabilities when you conducted twenty-five trials than when you conducted five trials, did you demonstrate the Law of Large Numbers in probability?
Go to the Unit 6: Assignment #2 and #4 Discussion Board and make a new Discussion Board post in which you do the following:
1. First, state which item you chose, how many of each variety were included, and the total number of the item.
2. Second, embed the photo you took of your ten items.
  - Remember to embed and size your photo using the procedures you learned from the Course How To.
  - NOTE: The Canvas Discussion Board cannot embed either .HEIC or .tiff/.tif images. Therefore, before trying to embed a .HEIC or .tiff/.tif image, you must save the image as a .jpg, .jpeg., or .png image.
3. Third, write an Image Description of your photo.
  - To learn how and why to write Image Descriptions, read Chen’s (2020) article, “How to Write an Image Description.”
  - Then, write an Image Description of your photo.
  - Post your Image Description underneath your embedded photo, so that it looks like this.
4. Fourth, embed the screenshot showing your three Frequency Distribution Tables (YourLastName_PSY-210_Unit06_Screenshot_Probability.xxx)
  - Remember to embed and size your screenshots using the procedures you learned from the Course How To.
5. Fifth, describe in two to three sentences the similarities and dissimilarities between your base-rate probabilities, your empirical probabilities when you conducted only five trials, and your empirical probabilities when you conducted twenty-five trials. Did you demonstrate the Law of Large Numbers in probability?

Unit 6: Assignment #3 (due before 11:59 pm Central on SAT JUL 6):

In this assignment, you will learn about independent versus dependent probabilities.
1. First, to learn, in general, the difference between independent versus dependent events, read Statistics How To’s (no date) article, “Dependent and Independent Events.”
  - When reading this article, write down two examples from the article of independent events and two examples from the article of dependent events.
  - Think of one more example of an independent event and one more example of a dependent event.
2. Second, to learn the difference between probabilities of independent versus dependent events, read Varsity Tutors’ (no date), article, “Independent vs. Dependent Probabilities.”
  - When reading this article, be sure you understand the difference between independent and dependent probabilities.
  - Make sure you notice how the probabilities change when two events (picking two marbles from a box) are independent versus when they are dependent.
OK, now you’re going to play a game called the Monty Hall Game. In this game, the game show host, whose name is Monty Hall, presents you with three doors. Behind two of the three doors are squeaking pigs, but behind one of the doors is the grand prize: a brand-new car, a dream vacation, and a ton of money! To win the grand prize, all you have to do is to pick the right door.
1. First, you choose one door of the three possible doors.
2. Second, without revealing what is behind the door you picked, Monty Hall reveals what’s behind one of the two doors that you didn’t pick. The door that Monty Hall reveals to you will always have a squeaking pig behind it.
3. Third, Monty Hall will give you two options: STAY with the unopened door you initially chose or SWITCH to the other unopened door.
  - Most people think it’s best to STAY with the door they initially picked, perhaps because they are faultily relying on their intuition that they must have initially selected the correct door.
  - But the probability of winning is much higher if you SWITCH to the other unopened door than if you STAY with the unopened door you initially chose.
  - In this assignment, you’re going to demonstrate that probability phenomenon to yourself, and you’re going to teach it to one other person.
Read these instructions and then click on this Monty Hall Game Simulator (note that it takes a few moments for the simulator to load).
1. First, as stated in the instructions, play 50 games during which you STAY with your initial choice.
  - Don’t worry! Each game requires only two simple clicks (of your mouse), which takes less than two seconds.
  - Therefore, playing 50 games takes less than two minutes!
2. Second, as stated in the instructions, capture with a partial screenshot (not a screenshot of your entire screen) the statistics about the 50 games in which you STAYED with your initial choice; save this screenshot with the filename YourLastName_PSY-210_Unit06_Screenshot_Stay01.xxx
3. Third, as stated in the instructions, play 50 games during which you SWITCH to the other door.
  - Again, don’t worry! Each game requires only two simple clicks (of your mouse), which takes less than two seconds.
  - Therefore, playing 50 games takes less than two minutes!
4. Fourth, as stated in the instructions, capture with a partial screenshot (not a screenshot of your entire screen) the statistics about each of your sets of games: the 50 games in which you SWITCHED to the other door; YourLastName_PSY-210_Unit06_Screenshot_Switch01.xxx
  - You’ll notice that these statistics include the “experimental probability” of each of your sets of games. Experimental probability is the same as empirical probability.
  - Remember, as you read in Poldrack’s chapter and as you demonstrated for yourself in Unit 6: Assignment #2, that empirical probability is observed probability.
  - Remember that the more samples you have, in this case, the more games you play, the more your empirical probability will match the base-rate probability (the Law of Large Numbers).
To learn the reason why the probability of winning is higher if you SWITCH than if you STAY, read Frost’s (no date), article, “The Monty Hall Problem: A Statistical Illusion.”
1. Try to follow the math (it’s not super hard).
2. Notice that the explanation for why the Monty Hall Game tricks even mathematicians and statisticians is because of our human reliance on intuition rather than on statistical thinking about probability.
Now, you’re going to teach one other person you know (a friend, family member, roommate, or the like) why statistical thinking about probability beats intuition.
1. Begin by describing the Monty Hall Game to this other person and asking this other person their intuition about whether they should SWITCH or STAY.
2. Do NOT yet tell this other person what you know about the probability of winning being higher if they switch.
3. Then, ask this other person to play 50 games during which they STAY with their initial choice.
  - Tell this person, not to worry! Each game requires only two simple clicks (of your mouse), which takes less than two seconds.
  - Therefore, playing 50 games takes less than two minutes!
4. Ask this person to capture with a partial screenshot (not a screenshot of their entire screen) the statistics about the 50 games in which they STAYED with their initial choice; you should save the screenshot this person gives you with the filename YourLastName_PSY-210_Unit06_Screenshot_Stay02.xxx
5. Next, ask this person to play 50 games during which they SWITCH to the other door.
  - Again, tell this person, not to worry! Each game requires only two simple clicks (of your mouse), which takes less than two seconds.
  - Therefore, playing 50 games takes less than two minutes!
6. Ask this person to capture with a partial screenshot (not a screenshot of their entire screen) the statistics about the 50 games in which they SWITCHED from their initial choice; you should save the screenshot this person gives you with the filename YourLastName_PSY-210_Unit06_Screenshot_Switch02.xxx
7. Finally, explain to this other person what you know about why the probability of winning is higher if you SWITCH than if you STAY and why statistical thinking about probability beats human intuition.
Go to the Unit 6: Assignment #3 Discussion Board and make a new Discussion Board post of at least 200 words in which you do the following:
1. Discuss your experience playing the Monty Hall Game, including your initial intuition, the empirical probabilities you observed, and your later-learned understanding of why the probability of winning increases if you switch.
2. Embed the two screenshots with the probabilities from your two sets of games (YourLastName_PSY-210_Unit06_Screenshot_Stay01.xxx and YourLastName_PSY-210_Unit06_Screenshot_Switch01.xxx). Remember to embed and size your screenshots using the procedures you learned from the Course How To.
3. Discuss your experience teaching another person about the Monty Hall Game, including this other person’s initial intuition, the empirical probabilities they observed, and their later-learned understanding (after you tutored them) of why the probability of winning increases if they switch.
4. Embed the two screenshots with the probabilities from this other person’s two sets of games (YourLastName_PSY-210_Unit06_Screenshot_Stay02.xxx and YourLastName_PSY-210_Unit06_Screenshot_Switch02.xxx). Remember to embed and size your screenshots using the procedures you learned from the Course How To.

Unit 6: Assignment #4 (due before 11:59 pm Central on SAT JUL 6):

Review from the Course How To, learn “How To Make a Reply to a Discussion Board Post.”
Review from the Course Syllabus, review “What’s the best way to respond to another student’s Discussion Board post?” Remember that your responses to other students should always include at least two of the four recommended components.
Go to the Unit 6: Assignment #2 and #4 Discussion Board and read ALL the other students’ posts. Then, make a response (a reply) to three other students’ posts.
1. Each of your three responses must be at least 200 words.
2. One response must be to a student whose ten items are most similar to yours; another response must be to a student whose ten items are least similar to yours; your third response can be to any other student.
3. If three other students in your section have not yet posted to the Discussion Board, you will need to wait until they do OR until the deadline for Unit 6: Assignment #4 has passed.
  - While you wait, you can (and should) work ahead to further assignments.

Unit 6: Assignment #5 (due before 11:59 pm Central on SUN JUL 7):

Meet online with your small Chat Group for a one-hour text-based Group Chat at the time and date that your Chat Group previously arranged. BEFORE MEETING ONLINE:
1. If your last name comes last alphabetically in your Chat Group:
  - Read Anderson’s (2019) article, “Polish Village Hasn’t Seen a Boy Born in Nearly 10 Years – Here’s How that Computes.”
    - While reading Anderson’s article, think about the Law of Large Numbers, which you learned about in Poldrack’s chapter, and the fact that “the empirical (or observed) probability will approach the base-rate probability as the sample size increases.”
  - Watch TEDEd’s (2015) video, “The Last Banana: A Thought Experiment in Probability.”
    - While watching TEDEd’s video, think about the contrast between independent and dependent (conditional) probability as you learned from reading Statistics How To’s article, which you read in Unit 6: Assignment #3.
2. If your last name comes first alphabetically in your Chat Group:
  - Read Mayyasi’s (2014) article, “Can An Athlete Be Streaky?”
    - While reading Mayyasi’s article, think about the difference between independent and dependent (or conditional) probability as you learned from reading Statistics How To’s article, which you read in Unit 6: Assignment #3.
  - Watch TEDEd’s (2017) video, “Check Your Intuition: The Birthday Problem.”
    - While watching TEDEd’s video, think about the contrast between intuitive probability and base-rate probability that you learned about from Professor Gernsbacher’s lecture video.
3. If you are in a Chat Group with three students, including yourself, and your last name comes neither first nor last alphabetically in your Chat Group:
  - Read Effectiviology’s (no date) article, “The Gambler’s Fallacy: On the Danger of Misunderstanding Simple Probabilities.”
    - While reading Effectivology’s article, think about the difference between independent and dependent (or conditional) probability as you learned from reading Statistics How To’s article, which you read in Unit 6: Assignment #3.
  - Watch TEDEd’s (2019) video, “Can You Outsmart this Logical Fallacy?”
    - While watching TEDEd’s video, think about the contrast between intuitive probability and base-rate probability that you learned about from Professor Gernsbacher’s lecture video.
4. If you are in a Chat Group with only two students, including yourself, and your last name comes last alphabetically in your Chat Group:
  - Read Effectiviology’s (no date) article, “The Gambler’s Fallacy: On the Danger of Misunderstanding Simple Probabilities.”
    - While reading Effectivology’s article, think about the difference between independent and dependent (or conditional) probability as you learned from reading Statistics How To’s article, which you read in Unit 6: Assignment #3.
5. If you are in a Chat Group with only two students, including yourself, and your last name comes first alphabetically in your Chat Group:
  - Watch TEDEd’s (2019) video, “Can You Outsmart this Logical Fallacy?”
    - While watching TEDEd’s video, think about the contrast between intuitive probability and base-rate probability that you learned about from Professor Gernsbacher’s lecture video.
IMPORTANT: While reading these articles and watching these videos, you can and should definitely write down important ideas. However, do NOT prepare multi-sentence summaries that you might later be tempted to copy/paste into the text chat. Your notes should only be ideas, not prepared comments or verbatim information from the articles or videos.
DURING your one-hour Group Chat:
1. Each Chat Group member will tell the other members of the Chat Group about the article(s) they read and the video(s) they watched.
2. Go in a round-robin order, so that one Chat Group member tells the other Chat Group members about only one of the articles they read or videos they watched; then another Chat Group member tells the other Chat Group members about only one article or video, and so forth until all Chat Group members have told the other Chat Group members about all the articles or videos — but doing so only one Chat Group member and one article or video at a time.
  - As mentioned above, do NOT have a prepared summary written out that you simply copy/paste into the text chat. Your telling the other Chat Group members about each article or video should be conversational and causal — not a prepared presentation.
  - Immediately after each Chat Group member tells the other Chat Group members about an article or video, the other Chat Group members are responsible for asking three questions about that article or video (and the Chat Group member who told about the article or video is responsible for answering those questions!).
AT THE END of your one-hour Group Chat:
1. Nominate one member of your Chat Group (who participated in the Chat) to make a post on the Unit 6: Assignment #5 Discussion Board that summarizes your Group Chat in at least 200 words. This Chat Group member should not post their 200-word summary of your Group Chat until they have completed their Course Journal for the current Unit.
  - At the end of the 200-word summary, this member needs to write this sentence filling the blanks: “I have completed my Course Journal for the current Unit. It contains ___ words and the two things I learned during this Unit about which I journaled about are ___ and ___.”
2. Nominate a member of your Chat Group (who participated in the Group Chat using the browser Chrome on their laptop, rather than on their mobile device) to save the Chat transcript, as described in the Course How To (under the topic, “How To Save and Attach a Chat Transcript”).
  - This member of the Chat Group needs to make a post on the Unit 6: Assignment #5 Discussion Board and attach the Chat transcript, saved as a PDF, to that Discussion Board post. This Chat Group member should not post the transcript of your Group Chat until they have completed their Course Journal for the current Unit.
    - In their Discussion Board post, this member needs to write this sentence filling the blanks: “I have completed my Course Journal for the current Unit. It contains ___ words and the two things I learned during this Unit about which I journaled about are ___ and ___.”
  - Remember to attach the Chat transcript by clicking on the word “Attach.” (Do not click on the sidebar menu “Files.”)
3. Nominate a third member of your Chat Group (who also participated in the Chat) to make another post on the Unit 6: Assignment #5 Discussion Board that states the name of your Chat Group, the names of the Chat Group members who participated in the Chat, the date of your Chat, and the start and stop time of your Group Chat. This Chat Group member should not post the names, date, and times of your Group Chat until they have completed their Course Journal for the current Unit.
  - In their Discussion Board post, this member needs to write this sentence filling the blanks: “I have completed my Course Journal for the current Unit. It contains ___ words and the two things I learned during this Unit about which I journaled about are ___ and ___.”
4. If only two students participated in the Chat, then one of those two students needs to do two of the above three tasks.
5. Before ending the Group Chat, arrange the date and time for the Group Chat you will need to hold during the next Unit (Unit 7: Assignment #5).

Congratulations, you have finished Unit 6! Onward to Unit 7!