Complement rule
$$P(A^c)=1-P(A)$$
Find the probability that an event does not occur.
High school · APProbability formulas, grouped by topic.
17 probability formulas across 6 topics, free and without an account. Probability formulas assign and combine likelihoods. The addition, multiplication, complement, and conditional rules build every joint and marginal probability you need, while the counting formulas supply the numerators and denominators. The named distributions — binomial, geometric, Poisson, normal, exponential — each apply only under a specific model of the experiment, so identifying the model matters more than recalling the algebra.
Every probability formula on one page
Each entry links to its own page, where the symbols are defined, the conditions are stated, and the formula is substituted through a worked example. Levels covered here: High school, AP, University.
Rules
3 formulas in rules.
Addition rule
$$P(A\cup B)=P(A)+P(B)-P(A\cap B)$$
Find the probability that at least one of two events occurs.
High school · APMultiplication rule
$$P(A\cap B)=P(A\mid B)P(B)$$
Find a joint probability using a conditional probability.
High school · APConditional probability
2 formulas in conditional probability.
Conditional probability
$$P(A\mid B)=\frac{P(A\cap B)}{P(B)}$$
Restrict probability to outcomes where $B$ occurred.
High school · AP · UniversityBayes’ theorem
$$P(A\mid B)=\frac{P(B\mid A)P(A)}{P(B)}$$
Reverse a conditional probability after observing evidence.
AP · UniversityCounting
2 formulas in counting.
Permutations
$$P(n,r)=\frac{n!}{(n-r)!}$$
Count ordered selections of $r$ distinct objects from $n$.
High school · APCombinations
$$\binom nr=\frac{n!}{r!(n-r)!}$$
Count unordered selections of $r$ objects from $n$.
High school · APDistributions
7 formulas in distributions.
Binomial probability
$$P(X=k)=\binom nkp^k(1-p)^{n-k}$$
Find exactly $k$ successes in $n$ independent Bernoulli trials.
High school · AP · UniversityBinomial mean and variance
$$E[X]=np,\qquad\operatorname{Var}(X)=np(1-p)$$
Summarize the center and spread of a binomial count.
AP · UniversityGeometric probability
$$P(X=k)=(1-p)^{k-1}p$$
Find the trial number of the first success.
AP · UniversityPoisson probability
$$P(X=k)=e^{-\lambda}\frac{\lambda^k}{k!}$$
Model event counts occurring at a constant average rate.
UniversityUniform distribution
$$X\sim U(a,b),\quad f(x)=\frac1{b-a},\quad E[X]=\frac{a+b}{2},\quad\operatorname{Var}(X)=\frac{(b-a)^2}{12}$$
Model an outcome equally likely across a finite interval.
High school · UniversityExponential distribution
$$f(x)=\lambda e^{-\lambda x},\quad E[X]=\frac1\lambda,\quad P(X>x)=e^{-\lambda x}$$
Model waiting time between constant-rate Poisson events.
UniversityHypergeometric probability
$$P(X=k)=\frac{\binom Kk\binom{N-K}{n-k}}{\binom Nn}$$
Find successes when sampling without replacement from a finite population.
AP · UniversityRandom variables
1 formula in random variables.
Expected value and variance
$$E[X]=\sum_x xP(X=x),\qquad\operatorname{Var}(X)=E[X^2]-E[X]^2$$
Find the long-run center and squared spread of a discrete random variable.
AP · UniversityEvents
2 formulas in events.
Law of total probability
$$P(B)=\sum_i P(B\mid A_i)P(A_i)$$
Combine conditional probabilities across every mutually exclusive case.
AP · UniversityIndependence test
$$A\perp B\iff P(A\cap B)=P(A)P(B)$$
Check whether knowing one event changes the probability of another.
High school · APKeep going with probability
A formula sheet is a reference, not a method. Use the subject guide to see where these relationships come from, a calculator to check a substitution you are unsure about, and practice questions to find out whether you can actually retrieve them.
- Study probability — the subject hub with lessons, worked methods, and common mistakes.
- Statistics calculator — enter your own values and compare the result with your working.
- Statistics Practice — retrieval practice across every topic listed above.
- Math formula library — search all 215 formulas by name, symbol, or condition.
Formulas in the other subjects
Mathematics does not stop at a subject boundary, and neither do its formulas. Each subject page below lists its own relationships, conditions, and worked examples.
Arithmetic
Review the core arithmetic relationships, their restrictions, and worked substitutions.
Algebra
Review the core algebra relationships, their restrictions, and worked substitutions.
Geometry
Review the core geometry relationships, their restrictions, and worked substitutions.
Trigonometry
Review the core trigonometry relationships, their restrictions, and worked substitutions.
Precalculus
Review the core precalculus relationships, their restrictions, and worked substitutions.
Calculus
Review the core calculus relationships, their restrictions, and worked substitutions.
Statistics
Review the core statistics relationships, their restrictions, and worked substitutions.
Linear Algebra
Review the core linear algebra relationships, their restrictions, and worked substitutions.
Differential Equations
Review the core differential equations relationships, their restrictions, and worked substitutions.
Discrete Math
Review the core discrete math relationships, their restrictions, and worked substitutions.