By Amanda Walker
(Grades 9-12+) This lesson, published in August of 2017, uses a probability game and computer simulations to explore the law of large numbers, conditional events, sampling distributions, and the central limit theorem. Video clips from “The Tonight Show” are shown to students in which Jimmy Fallon plays the egg roulette game with celebrities.
Students play the game and are asked several questions regarding the probabilities of winning. The class data is used to estimate an unknown probability. Part I of the lesson uses a preconstructed Fathom simulation to collect more data, estimate an unknown probability, and demonstrate the law of large numbers. A discussion of how to calculate the probability follows. In Part II of the lesson, a free online computer applet is used to display the sampling distribution of a sample proportion by using the assumed probability obtained in Part I. Students explore variability, mean, and properties of an empirical sampling distribution. Applications of the central limit theorem are discussed using extensions of the egg roulette game.
The main goals of this lesson are to: (1) recognize conditional probabilities; (2) understand an unknown probability can be estimated using the law of large numbers; and (3) construct and explore the variability of sampling distributions and central limit theorem using randomization-based simulations.
Keywords: Grades 9-12+, conditional probability, sampling distributions, law of large numbers, central limit theorem