Lesson 2.1: Probabilities of Events
Lesson Learning Objectives
- Understand the basic concepts of probability.
- Apply the definition of probability to find the probability of a particular outcome occurring.
- Calculate probabilities from equally likely sample spaces.
- Calculate probabilities using the Addition Rule of disjoint outcomes.
- Calculate probabilities using the General Addition Rule.
- Calculate probabilities using the Complement Rule.
- Calculate probabilities using the Multiplication Rule for independent processes.
Lesson 2.1 Checklist
| Learning activity | Graded? | Estimated time |
|---|---|---|
| Read OpenIntro Statistics section 3.1 and supplementary notes | No | 30 mins |
| Watch instructional video | No | 20 mins |
| Answer two lesson check-in questions | Yes | 15 mins |
| Work through virtual statistical software lab | No | 45 mins |
| Answer two virtual statistical software lab questions | Yes | 15 mins |
| Work on practice exercises | No | 1.5 hours |
| Explore suggested websites | No | 15 mins |
Learning Activities
Readings 📖 and Instructional Video 🎦
Defining Probability
Read Section 3.1: Defining Probability in OpenIntro Statistics (Diez et al., 2019) CC BY-SA 3.0. Probability forms the foundation of statistics and this section gives a formal introduction to the topic. As you read, look up new terminology in the Glossary, and self-assess your understanding by attempting the guided practice exercises.
Watch the following video, Probability Introduction (OpenIntro Textbook Supplement) (Diez, 2016), on this topic (duration 00:19:51):
Basic Probability Concepts
Read Supplementary Notes 2.1, which reinforces the basic ideas of probability.
Lesson Check-in Questions ✍
Virtual Statistical Software Lab 💻
Work through the virtual statistical software lab: Software Lab 2.1: Probability Basics. This lab will guide you through some basic probability calculations using the examples of rolling a die and selecting a playing card. As you work through the lab, answer the exercises in the shaded boxes. These exercises are not graded but the solutions are available: Software Lab 2.1 Solutions. The lab should take you no more than 45 minutes to complete.
Virtual Statistical Software Lab Questions ✍
Practice Exercises 🖊
Work on the following exercises in OpenIntro Statistics: Exercises 3.1, 3.3, 3.5, 3.7, 3.9, and 3.11 and Chapter Exercise 3.39 (Diez et al., 2019) CC BY-SA 3.0. Check your answers using these solutions (Diez et al., 2019) CC BY-SA 3.0. You’ll deepen your understanding much more effectively if you genuinely attempt the questions by yourself before checking the solutions.
Work on the WeBWorK exercises, which are linked from your Moodle course. Check your answers using the solutions provided.
Suggested Websites 🌎
- Faculty and students at the University of Regina maintain the Aboriginal Perspectives website, which contains information to aid teachers in including Indigenous perspectives in their lessons. Included there are Games from the Aboriginal People of North America (Treptau et al., n.d.) that rely on the concepts of data management and probability.
- TED, which began in 1984 as a conference where Technology, Entertainment and Design converged, is a nonprofit most famous for its TED Talks. TED-Ed, which is TED’s youth and education initiative, produce short, animated videos on a variety of subjects, including data analysis and probability. There’s a lot of useful content here, but of particular relevance to this lesson is the video titled The Last Banana: A Thought Experiment in Probability (Barichello, 2015) (duration 00:04:10):
Media Attribution
Dice, by Steve A. Johnson (2011), on Flickr, CC BY 2.0
References
Barichello, L. (2015, Feb. 23). The last banana: A thought experiment in probability [Video]. YouTube. https://www.youtube.com/watch?v=Kgudt4PXs28
Diez, D. [OpenIntroOrg]. (2016, Dec. 7). Probability introduction (OpenIntro textbook supplement) [Video]. YouTube. https://www.youtube.com/watch?v=rG-SLQ2uF8U
Diez, D. M., Çetinkaya-Rundel, M., Barr, C. D. (2019). OpenIntro Statistics (4th ed.). OpenIntro. https://www.openintro.org/book/os/
Johnson, Steve. [Steve A Johnson]. (2011). Dice [Photograph]. Flickr. https://flic.kr/p/9BdSve
Treptau, C., Arnason, K., Maeers, M., McDonald, J. & Weston, H. (n.d.). Games from the Aboriginal People of North America. Aboriginal Perspectives. https://www.aboriginalperspectives.uregina.ca/games/
