AP Statistics Unit 4 Progress Check Probability, Random Variables and Probability Distributions walkthrough.
AP Statistics Unit 4 is probability and random variables, and the Unit 4 Progress Check MCQ is where students first confuse binomial with geometric and assume independence that was never given. This walkthrough covers the question types, the traps, and how to reason through them. Explanations only — no AP Classroom answer keys.
What Unit 4 covers
Unit 4 is Probability, Random Variables and Probability Distributions. Probability and random variables is roughly 10–20% of the AP Statistics exam — one of the widest weightings in the course.
The Progress Check MCQ: what each question type tests
These are the question patterns that recur on this Progress Check, and what each one is really asking.
The Progress Check FRQ
Unit 4 free response usually asks for a probability calculation plus an interpretation. Points come from showing which rule or distribution you used, justifying independence when you rely on it, and interpreting expected value as a long-run average rather than a prediction for one trial.
Where students lose the most points
How to work through this unit
Before choosing a distribution, ask one question: is the number of trials fixed? Yes means binomial, no means geometric. That single check resolves most Unit 4 confusion.
Once you have finished the Progress Check, put your raw score into our AP Statistics Calculator to see roughly where that pace puts you on the 1–5 scale, and use the AP Statistics Review for the full exam format and study plan.
Frequently asked questions
Quick answers — written by humans, not a chatbot.
What does the AP Statistics Unit 4 Progress Check cover?
Probability rules, conditional probability, independence, discrete random variables and expected value, combining random variables, and the binomial and geometric distributions.
What is the difference between binomial and geometric?
Binomial has a fixed number of trials and counts successes. Geometric counts the number of trials until the first success, so the number of trials is not fixed.
Can I add standard deviations when combining random variables?
No. Means add directly, but you must add variances — and only when the variables are independent — then take the square root.
Do you publish AP Statistics Unit 4 answers?
No. We publish walkthroughs of the reasoning and common traps rather than AP Classroom answer keys.