Using Scratch-Off Lottery Tickets to Teach Binomial Probabilities and Expected Value

Abstract

This paper demonstrates how to use state lottery scratch-off tickets as an interactive classroom exercise to explain the binomial distribution and expected value. Students often struggle to comprehend how theoretical probability distributions relate to empirical outcomes. One way to improve student engagement and understanding is by using relatable interactive classroom exercises. The exercise in this paper involves every student receiving a lottery ticket, calculating binomial probabilities and using this information to estimate expected value, average payout, standard deviation, and the number of winners. We then compare the empirical results with what we observe after all the tickets are scratched.