The Geometric Distribution Practice Test

A student practices free throws and records each attempt as “made” or “missed.” The student keeps shooting until making the first free throw, then stops. Assume the chance of making any given free throw stays the same from shot to shot and each shot outcome is independent. The student wants to model the number of shots taken until the first made free throw. Why is a geometric model appropriate?

A researcher administers a short survey to randomly selected people walking through a mall until the first person agrees to participate. Each person either “agrees” or “declines,” and the researcher stops after the first agreement. Assume the probability a person agrees is approximately constant and each selection is independent. The researcher wants to model the number of people asked until the first agreement. Why is a geometric model appropriate?