Week 9
Modelling Uncertainty: Probability

Business

The start of the week email.

⦿ Monday: Simple probability and tree diagrams

Introduction to probability Pencast 6:54 | PDF
Uncertainty surrounds us. Probability gives us the tools to model it. First we need to recognize the language that tips us off to the presence of uncertainty and particularly of probabilities: "chance", "odds" and of course "probability" itself. These terms all refer to fractions. This implies that probabilities will always have decimal values between 0 and 1, and that the total probability of an event happening or not happening must be 1.0.
Simple Probabilities Pencast 7:51 | PDF
We begin with "simple" probability, i.e. the probability of discrete or atomic events, and consider coin tosses, dice rolls and dealing cards.
Example: Two dice Pencast 8:51 | PDF
Rolling two dice presents us with our first example of probability subtlety, emphasizes the importance of identifying equiprobable events, and provides our first model for compound events: a table of possibilities.
Example: Coin tossing Pencast 12:21 | PDF
Tossing a coin once is not the interesting, but what about the outcomes of multiple tosses? A second modelling tool, tree diagrams, help us map out the possibilities.
Example: Basketball free throws Pencast 6:05 | PDF
How many points can we expect our 69% free throw shooter to get in a one-and-one?
Example: The playoffs Pencast 7:46 | PDF
One team wins 3 of 4 regular season meetings with another. What is the probability they win a best of 3 playoff series?
Tree algebra Pencast 5:05 | PDF
We've been working with tree diagrams intuitively. Let's formalize the rules.
The Chevalier de Méré's question Pencast 10:13 | PDF
We've finally accumulated the tools necessary to answer the Chevalier de Méré's question. Was he right?

Exercises

If you're comfortable with the topics above you're ready to work on:

Supplementary resources:

In Introductory Statistics from OpenStax
Chapter 3 covers this week's probability topics.

Chapter 3 in College Mathematics for Everyday life by Inigo, Jameson, Kozak, Lanzetta, and Sonier. It's a simpler presentation, but sadly doesn't have a table of contents for the chapter so you have to scroll to find what you want.

⦿ Wednesday: Conditional probability and Bayes' theorem

Independence and conditional probability Pencast 9:55 | PDF
The nice thing about coins and dice is that they don't know what happened on the previous toss or roll, but people and lots of systems do. That means we sometimes have to work with conditional instead of independent probabilities.
Example: Colour blindness Pencast 11:03 | PDF
Colour blindness is not evenly distributed across the sexes, which affects the odds of men and women being colour blind.
Bayes' Theorem Pencast 4:25 | PDF
Often we have a posterior condition, like a test result, and want to know what it tells us about the probability of a prior condition, like the presence of a disease.
Example: Tuberculosis screening Pencast 11:39 | PDF
You are randomly selected to be tested for tuberculosis. The test result is positive. Should you be worried?
Example: That beetle! Pencast 11:12 | PDF
You find a beetle with rare markings. Does that make it a rare beetle?

Exercises

If you're comfortable with the topics above you're ready to work on:

Supplementary resources:

In Introductory Statistics from OpenStax
Chapter 3 covers this week's probability topics.

Chapter 3 in College Mathematics for Everyday life by Inigo, Jameson, Kozak, Lanzetta, and Sonier. It's a simpler presentation, but sadly doesn't have a table of contents for the chapter so you have to scroll to find what you want.

⦿ Friday: Reading break begins ⇒ No classes 😔

Assignment

Assignment 9 is posted. Due by 1 pm Friday March 20. Note that the problems are worth different numbers of marks. Use your time wisely.

Name the file you submit A9_firstname.pdf, e.g.

A9_Tim.pdf

If you have to submit multiple files, add a suffix number to each, e.g.

A9_Tim_1.pdf
A9_Tim_2.pdf