Probability Calculator
Calculate event probabilities, odds ratios, and percentage chances.
GCD & LCM Calculator
About Probability Calculator
The Comprehensive Probability Calculator calculates single-event probabilities ($P(A) = \frac{n(A)}{n(S)}$), compound independent/dependent events ($P(A \cap B)$), mutually exclusive events ($P(A \cup B)$), conditional probability ($P(A|B)$), and odds-to-probability conversions.
How to Use Probability Calculator
Step 1
Select probability mode (Single, Compound Independent, or Series).
Step 2
Enter event probabilities or favorable/total outcome counts.
Step 3
Inspect union, intersection, complement, and odds results.
Step 4
Click "Copy Result".
Practical Use Cases for Probability Calculator
Game Design & Board Game Mechanics
Calculate exact probabilities of dice rolls (e.g. rolling at least one 6 on three D6 dice: $1 - (5/6)^3 = 42.13\%$) and card draws.
Risk Assessment & Decision Science
Model independent success probabilities across repeated trials and evaluate conditional Bayesian risk factors.
Input & Output Examples
Calculating Probability of Two Independent Events
P(A) = 0.40, P(B) = 0.50 (Independent)
Union $P(A \\cup B) = 0.70$ (70%) | Intersection $P(A \\cap B) = 0.20$ (20%) | Odds in Favor: 7 to 3
Key Features & Performance
- ✓Event modes: Single Event, Independent Events ($A$ and $B$), Mutually Exclusive, and Conditional Probability ($P(A|B)$).
- ✓Series probability: probability of at least one success in $n$ independent trials ($1 - (1-p)^n$).
- ✓Converts between Probability (0 to 1), Percentage (0% to 100%), and Odds (e.g. 3 to 1).
- ✓100% Client-Side calculation.
- ✓1-Click Copy probability report.
Key Terminology & Definitions
Complement Rule
The probability that an event will not occur: $P(A') = 1 - P(A)$.
Conditional Probability ($P(A|B)$)
The probability of event $A$ occurring given that event $B$ has already occurred: $P(A|B) = \\frac{P(A \\cap B)}{P(B)}$.