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How accurate should government surveillance be?

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False Flags

How accurate should government surveillance be?

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Falseflags lessonpage
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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.

REAL WORLD TAKEAWAYS

  • United States National Security Agency (NSA) conducts a global surveillance program called PRISM in which they collect online communications, including from Americans who weren’t/aren’t aware.
  • At some points in time, this government surveillance has been controversial: It’s intended to flag dangerous individuals and monitor their communications to keep America safe, but it may also flag innocent individuals.

MATH OBJECTIVES

  • Model related probabilistic events using Venn diagrams
  • Apply Bayes Theorem given conditional probabilities
  • Use probabilities to predict the consequences of a real-world policy

Appropriate most times as students are developing conceptual understanding.
Lesson gauge medium
Algebra 2
Probability (Adv.)
Lesson gauge medium
Algebra 2
Probability (Adv.)
Mathematical Practices S.CP.3 Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. S.CP.5 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer. S.CP.8 (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model. S.MD.7 (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).
Content Standards MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics.

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