The Geometric Distribution

The Geometric Distribution is topic 4.12 of AP Statistics, inside Probability, Random Variables, and Probability Distributions. This page works through three real practice questions on it, with the full reasoning behind each credited answer.

Practise this topic freeThe whole unit
64 questionsUsing Probability and Simulation100% with a figure
Worked examples

Three real the geometric distribution questions

From the practice pool, not the mock papers — each with the reasoning that produces the answer.

64 practice questions sit on this single topic — enough that it is worth working through by topic rather than meeting it scattered through a unit review.

100% of them come with a figure. Reading the graph or diagram correctly is most of the work here before any content knowledge applies.

100% test a single AP skill: Using Probability and Simulation. That makes this topic unusually predictable to prepare for.

Using Probability and Simulation · with figure

Each independent trial has success probability 0.25. What is the probability that the first customer survey response occurs on trial 4?

  1. A0.8945
  2. B0.3164
  3. C0.0039
  4. D0.1055correct
  5. E0.25
Why D is correct

First success on trial 4 means 3 failures followed by success: (0.75)^3(0.25) = 0.1055.

geometric probability for first customer survey response: in the "Each independent trial has success probability 0.25. What is the probability that the first customer survey response occurs on trial 4?" setting, especially first customer survey response; survey response, match the probability rule to the event wording before calculating. The professional check is to keep the values 0.25, 4, the geometric probability method, and the final answer choice aligned with Probability, Random Variables, and Probability Distributions.

Using Probability and Simulation · with figure

Each independent trial has success probability 0.12. What is the probability that the first machine alert occurs on trial 6?

  1. A0.9367
  2. B0
  3. C0.4644
  4. D0.12
  5. E0.0633correct
Why E is correct

First success on trial 6 means 5 failures followed by success: (0.88)^5(0.12) = 0.0633.

geometric probability for first machine alert: in the "Each independent trial has success probability 0.12. What is the probability that the first machine alert occurs on trial 6?" setting, especially first machine alert; machine alert, match the probability rule to the event wording before calculating. The professional check is to keep the values 0.12, 6, the geometric probability method, and the final answer choice aligned with Probability, Random Variables, and Probability Distributions.

Using Probability and Simulation · with figure

Each independent trial has success probability 0.2. What is the probability that the first correct practice guess occurs on trial 3?

  1. A0.128correct
  2. B0.872
  3. C0.2
  4. D0.512
  5. E0.008
Why A is correct

First success on trial 3 means 2 failures followed by success: (0.8)^2(0.2) = 0.128.

geometric probability for first correct practice guess: in the "Each independent trial has success probability 0.2. What is the probability that the first correct practice guess occurs on trial 3?" setting, especially first correct practice guess; practice guess, match the probability rule to the event wording before calculating. The professional check is to keep the values 0.2, 3, the geometric probability method, and the final answer choice aligned with Probability, Random Variables, and Probability Distributions.

64 questions on this topic, free to start.

Ten a day at no cost. One account covers SAT, ACT and AP.

Start free
Last reviewed 2026-08-28. Topic and unit names follow the College Board course framework. Question counts describe the PrepScore practice bank, not the exam.

Work the geometric distribution until the reasoning is automatic.

Real AP questions with a full explanation on every answer, and a mistake bank that only clears when you get it right.

Start freeBack to the unit