This page covers Probability at the AP / College Prep level, delivered as a formula cheat sheet. Sample spaces, combinatorics, conditional probability, and stochastic processes. The mathematical la. The material here corresponds to Grades 11–12 courses: AP Calculus AB and AP Calculus BC.
The key formulas for Probability at the AP / College Prep level are organised below. Each formula is accompanied by a note on when it applies and what common variations exist.
The skills covered by these formulas are: Counting principles, Conditional probability, Bayes theorem, Random variables, Distributions.
For each formula, read the conditions carefully. Many errors in Probability come from applying a formula outside its domain of validity — using a geometric formula that assumes a right angle when the angle is not specified, or applying a probability rule that requires independence when the events are dependent.
Use this sheet as a revision tool after you have worked through problems — not as a first introduction to the material. A formula you have derived or used is one you will remember; a formula you have only read is one you will forget under exam pressure.
Worked Example
A standard probability problem at the ap college prep level.
Work through step by step: identify what is given, what is asked, apply the relevant technique, and check your answer against the original conditions.
Confusing P(A|B) with P(B|A) — the prosecutor's fallacy. These are rarely equal and require Bayes' theorem to relate to each other.
Frequently Asked Questions
How is Probability different at the AP / College Prep level compared to earlier levels?
At the AP / College Prep level, Probability builds on Grades 11–12 prerequisites. Students are expected to have completed AP Calculus AB before tackling this material.
Which exams test Probability at this level?
AP Statistics, GRE, Actuarial exam prep.
What is the single most effective way to practise Probability for AP / College Prep students?
The most effective practice at the AP / College Prep level is deliberate work on novel problem setups — not repeated drilling of the same template. Attempt problems before looking at solutions, and review errors by identifying the specific step where the reasoning broke down.