Probability Calculator
Calculate probabilities for various scenarios including basic probability, conditional probability, combinations, permutations, and common probability distributions.
Select Probability Type
Basic Probability
Simple event probability
Conditional
P(A|B) calculations
Binomial
Success/failure trials
Combinations
Choose without order
Permutations
Arrange with order
Normal Distribution
Bell curve probabilities
Results
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0.00%
Probability
How to Use the Probability Calculator
Probability measures the likelihood of an event occurring, expressed as a value between 0 (impossible) and 1 (certain). Our comprehensive calculator handles six major types of probability calculations: Basic Probability for simple event likelihood, Conditional Probability for dependent events, Binomial Distribution for repeated success/failure trials, Combinations for selecting items without regard to order, Permutations for arrangements where order matters, and Normal Distribution for continuous data following a bell curve pattern. Select your calculation type, enter the required parameters, and get instant results with visual representations and detailed breakdowns.
Basic Formulas:
Basic Probability: P(A) = Number of favorable outcomes / Total outcomes
Conditional: P(A|B) = P(A ∩ B) / P(B)
Combinations: C(n,r) = n! / (r!(n-r)!)
Binomial: P(X=k) = C(n,k) × p^k × (1-p)^(n-k)
Basic Probability: P(A) = Number of favorable outcomes / Total outcomes
Conditional: P(A|B) = P(A ∩ B) / P(B)
Combinations: C(n,r) = n! / (r!(n-r)!)
Binomial: P(X=k) = C(n,k) × p^k × (1-p)^(n-k)
🎲 Practical Example:
Scenario: Rolling two dice and getting a sum of 7
Favorable outcomes: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 ways
Total outcomes: 6 × 6 = 36 possible combinations
Probability: 6/36 = 1/6 ≈ 0.1667 or 16.67%
Application: This calculation helps understand gambling odds, game theory, and risk assessment in various fields.
Mastering probability calculations is essential for statistics, data science, risk management, and decision-making under uncertainty. Whether you're analyzing survey data, predicting outcomes, designing experiments, or making business decisions, understanding probability helps quantify uncertainty and make informed choices. Our calculator provides step-by-step breakdowns and visual aids to help you understand not just the final probability, but also the reasoning behind each calculation, making it an excellent learning tool for students and professionals alike.