The Happy Meal has become an American institution. Burgers, fries, nuggets, and, of course, toys. Trying to collect a whole set can be fun…and sometimes frustrating. In this lesson, we’ll use probability and expected value to figure out how many Happy Meals you should plan on buying if you just have to get all of those sweet knickknacks.

You might recognize this as the Coupon Collector’s problem, but come on, that’s no fun at all. Have you ever tried to play with a coupon? It’s terrible. Also, paper cuts are the worst.

### Students will

• Model Bernoulli trials with dice
• Create frequency histograms from experimental data and interpret the results
• Calculate the theoretical probabilities for completing a set of Happy Meal toys
• Use probability and expected value to calculate the average number of purchases required to complete a set of toys, and compare this with conjectures based on empirical results

### Before you begin

Students should be familiar with the basic concepts of probability, including independence and the probabilities of compound events. If students know how to obtain expected value from probability in a Bernoulli setting, then they will find the theoretical work easier, but we approach expected value in a strongly intuitive way, so it’s certainly not a prerequisite for working through the lesson.