Basic probability

Basic Probability Formulas

Probability Range

0 ≤ P(A) ≤ 1

Rule of Complementary Events

P(AC) + P(A) = 1

Rule of Addition

P(A∪B) = P(A) + P(B) - P(A∩B)

Disjoint Events

Events A and B are disjoint iff

P(A∩B) = 0

Conditional Probability

P(A | B) = P(A∩B) / P(B)

Bayes Formula

P(A | B) = P(B | A) ⋅ P(A) / P(B)

Independent Events

Events A and B are independent iff

P(A∩B) = P(A) ⋅ P(B)

Cumulative Distribution Function

FX(x) = P(Xx)

Probability Mass Function

sum(i=1..n, P(X=x(i)) = 1

Probability Density Function

fX(x) = dFX(x)/dx

FX(x) = integral(-inf..x, fX(y)*dy)

FX(x) = sum(k=1..x, P(X=k))

P(a<=X<=b) = integral(a..b, fX(x)*dx)

integral(-inf..inf, fX(x)*dx) = 1

Covariance

Cox(X,Y) = E(X-ux)(Y-uy) = E(XY) - ux*uy

Correlation

corr(X,Y) = Cov(X,Y)/(Std(X)*Std(Y))

Bernoulli: 0-failure 1-success

Geometric: 0-failure 1-success

Hypergeometric: N objects with K success objects, n objects are taken.

 


Currently, we have around 929 calculators and conversion tables to help you "do the math" quickly in areas such as:

And we are still developing more. Our goal is to become the one-stop, go-to site for people who need to make quick calculations or who need to find quick answer for basic conversions.

Additionally, we believe the internet should be a source of free information. Therefore, all of our tools and services are completely free, with no registration required. We coded and developed each calculator individually and put each one through strict, comprehensive testing. However, please inform us if you notice even the slightest error – your input is extremely valuable to us. While most calculators on Justfreetools.com are designed to be universally applicable for worldwide usage, some are for specific countries only.


This website uses cookies to improve your experience, analyze traffic and display ads. Learn more