Done

๐ŸŽฒ Probability Calculator

Calculate single/multiple event, binomial, permutation, combination, Bayes' theorem, dice & coin probabilities โ€” with step-by-step solutions.

Probability Calculator
โ€”
Formula & Steps
Calculation Log
; TechOreo Probability Calculator
; Step-by-step solutions
; โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€โ”€
; Select a mode and enter values to calculate
History
No calculations yet
Quick Examples
๐ŸŽฒ Rolling a 6
P = 1/6 โ‰ˆ 16.67%
๐Ÿƒ Drawing an Ace
P = 4/52 โ‰ˆ 7.69%
๐Ÿช™ Two Heads in a Row
P = 0.5 ร— 0.5 = 25%
๐Ÿ“Š 7 Heads in 10 Flips
P(X=7) โ‰ˆ 11.72%
๐Ÿƒ Poker Hands (5 from 52)
C(52,5) = 2,598,960
๐Ÿฅ Medical Test (1% disease)
P(disease|positive) โ‰ˆ 16.1%
Shortcuts
Ctrl+โ†ตCalculate
Alt+RReset
Alt+CCopy result
Alt+1-6Switch mode
Formula Reference
P(A) = favorable / total
Single event probability
P(AโˆฉB) = P(A) ร— P(B)
Independent events (AND)
P(AโˆชB) = P(A) + P(B) โˆ’ P(AโˆฉB)
Union (OR) for non-exclusive events
C(n,r) = n! / (r!(nโˆ’r)!)
Combinations (order doesn't matter)
P(A|B) = P(B|A)ยทP(A) / P(B)
Bayes' theorem

About Probability Calculations

Basic Probability

Probability measures how likely an event is to occur, ranging from 0 (impossible) to 1 (certain). It equals favorable outcomes divided by total possible outcomes for equally likely events.

Binomial Distribution

Models the number of successes in a fixed number of independent yes/no trials, each with the same probability. Used for coin flips, quality control, survey responses, and more.

Combinations & Permutations

Combinations count selections where order doesn't matter (lottery). Permutations count arrangements where order matters (rankings). Both are fundamental to counting and probability.

Bayes' Theorem

Updates the probability of an event based on new evidence. Widely used in medical testing, spam filtering, machine learning, and decision-making under uncertainty.