Ch-ch-ch-changes! Mathalicious is now Citizen Math . Please visit www.CitizenMath.com for the real-world math lessons you know and love. Alternatively, you can continue to access Mathalicious.com until the end of the school year, at which point Mathalicious will ride off into the sunset. For more details about the transition to Citizen Math, please click here.
Is it ever a good idea to buy an extended product warranty? In this lesson students use percents to explore the expected value of AppleCare, i.e. how much is AppleCare actually worth, and how much does it cost?

This expected value depends on two factors: the probability that the device will break and the cost to replace it. The higher the probability that a product will fail, and the more expensive it is, the more valuable a warranty will be. So what does the probability of breaking have to be to justify purchasing AppleCare…and are warranties ever a good idea?

Students will

  • Understand that expected value offers consumers a way to quantify the value of a product warranty
  • Given price and probability of failure, calculate the expected value of AppleCare for various devices
  • Consider variables that vary directly and inversely (although use of that vocab is optional)
  • Examine how terms and conditions affect the expected value of a product warranty
  • Given the price of a device and its warranty, determine the probability of failure required to justify AppleCare

Before you begin

Students need to know how to calculate a given percent of a number, e.g., 20% of $1000 = 0.2 × $1000 = $200. They should also be able to find an unknown percent given a number and the result, e.g. What percent of $1000 is $200?

Common Core Standards

Content Standards
Mathematical Practices