How accurate should government surveillance be? In 2013, it was revealed that the U.S. government was secretly monitoring its citizens’ phone calls and internet traffic through a program called PRISM. The goal was to identify potential threats and catch would-be terrorists.
In this lesson, students calculate conditional probabilities to determine the likelihood of false-positives and false-negatives, and discuss the tradeoffs between safety and accuracy.
Model related probabilistic events using Venn diagrams
Apply Bayes Theorem given conditional probabilities
Use probabilities to predict the consequences of a real-world policy
Before you begin
Students should have a solid grasp of simple theoretical probabilities before beginning.
When is it worth buying a Powerball ticket? Students count combinations and apply basic rules of probability and expected value to determine when the Powerball jackpot is large enough to justify the cost of playing the game.
Conditional Probability and the Rules of Probability (CP)
When should NFL teams go for it on fourth down? Students use quadratic functions to develop a model of expected points. They then apply this model to determine when teams should punt the ball, and more importantly, when they shouldn’t.
Building Functions (BF), Interpreting Functions (IF), Using Probability to Make Decisions (MD)
Is there evidence of racial bias in death penalty sentencing? Students analyze almost thirty years’ worth of data summarized in frequency tables and discuss whether they see evidence of racial bias in who receives the death penalty and who doesn’t.
Conditional Probability and the Rules of Probability (CP), Interpreting Categorical and Quantitative Data (ID)
How much would it cost to get all the toys in a Happy Meal? Students use trials, probabilities, and expected value to determine how many meals it takes to get a complete set of Happy Meal toys and debate whether McDonald’s should allow customers to pay a fee to choose their own figurine.
Conditional Probability and the Rules of Probability (CP), Interpreting Categorical and Quantitative Data (ID), Making Inferences and Justifying Conclusions (IC)
Should airlines overbook their flights? Students use compound probability and expected value to determine the optimal number of tickets an airline should sell and discuss whether airlines should be allowed to overbook their flights.
Conditional Probability and the Rules of Probability (CP), Creating Equations (CED), Using Probability to Make Decisions (MD)
How have video game consoles changed over time? Students create exponential models to predict the speed of video game processors over time, compare their predictions to observed speeds, and consider the consequences as digital simulations become increasingly lifelike.
Building Functions (BF), Interpreting Categorical and Quantitative Data (ID), Interpreting Functions (IF), Linear, Quadratic, and Exponential Models (LE), Seeing Structure in Expressions (SSE)