Free forever Calculate score
AP Stats · Unit 4 Progress Check

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.

Updated August 2026Written by Mahmudul HasanFree · No signup

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.

Probability rules
Addition and multiplication rules, complements, and mutually exclusive versus independent.
Conditional probability
P(A|B) and how to read a two-way table or tree diagram.
Independence
Testing whether P(A|B) equals P(A) rather than assuming it.
Random variables
Discrete and continuous, expected value, and variance.
Combining random variables
Means always add; variances add only when the variables are independent.
Binomial and geometric
Fixed number of trials counting successes versus trials until the first success.

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.

Binomial or geometric?
Fixed n and counting successes is binomial. Counting trials until the first success is geometric.
Conditional probability from a table
Restrict to the given row or column first, then divide.
Independence check
Compare P(A|B) with P(A). If they differ, the events are dependent.
Expected value
Multiply each value by its probability and sum. Interpret it as a long-run average.
Combining variables
Add means directly, but only add variances when independence is stated.

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

Assuming independence
It must be given or justified. Sampling without replacement from a small population breaks it.
Confusing mutually exclusive with independent
Mutually exclusive events cannot both happen; independent events do not affect each other. They are not the same.
Adding standard deviations
Variances add for independent variables; standard deviations do not.
Mixing binomial and geometric
Check whether the number of trials is fixed before choosing.
Treating expected value as a guaranteed outcome
It is a long-run average and may not even be a possible value.

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.

Related

Keep going.

Scroll to Top