Probability Calculator

Professional probability calculator for combinations, permutations and statistical analysis

Probability Results

0.167 Probability
Probability (Decimal): 0.167
Probability (Percentage): 16.67%
Probability (Fraction): 1/6
Odds Against: 5:1

Calculation Steps:

1. Enter event parameters to see calculation steps

Combinatorics Results

120 Combinations
Formula Used: nCr = n!/(r!(n-r)!)
Total Items (n): 10
Selected Items (r): 3
Result: 120

Calculation Steps:

1. Enter values to see detailed calculation

Binomial Probability

0.1172 Probability
Trials (n): 10
Successes (k): 3
Success Probability: 0.5
Result (%): 11.72%

Formula:

P(X = k) = C(n,k) × p^k × (1-p)^(n-k)
1. Enter parameters to see step-by-step calculation

Conditional Probability

0.30 P(A|B)
P(A): 0.30
P(B): 0.40
P(A ∩ B): 0.12
Result: 0.30

Formula:

P(A|B) = P(A ∩ B) / P(B)
1. Enter probability values to see calculation

How to Use the Probability Calculator

Our comprehensive probability calculator provides four powerful tools for statistical analysis and probability calculations with detailed step-by-step solutions:

🎲 Basic Probability

Calculate fundamental probabilities for single and multiple events. Includes specialized calculators for dice rolls and card draws. Perfect for understanding basic probability concepts, determining odds, and solving everyday probability problems. Shows results in decimal, percentage, fraction, and odds formats.

🔢 Combinations & Permutations

Compute combinations (nCr), permutations (nPr), and factorials with detailed explanations. Essential for counting problems, lottery calculations, and arrangement problems. Automatically determines whether order matters and applies the appropriate formula with complete step-by-step breakdowns.

📊 Binomial Probability

Calculate probabilities for binomial distributions - scenarios with fixed number of independent trials, each with the same probability of success. Ideal for quality control, medical testing, survey analysis, and any repeated experiment with binary outcomes.

🔗 Conditional Probability

Analyze conditional probabilities and test for independence between events. Calculate P(A|B), P(A∪B), and determine if events are independent. Critical for Bayesian analysis, medical diagnosis, risk assessment, and any scenario involving dependent events.

🌟 Key Features

• Multiple Output Formats: Decimal, percentage, fraction, and odds representations
• Step-by-Step Solutions: Complete mathematical explanations for every calculation
• Interactive Examples: Built-in scenarios for dice, cards, and common probability problems
• Formula Reference: Clear display of mathematical formulas used
• Educational Value: Perfect for students, teachers, and professionals
• Accurate Calculations: Precise results using proper statistical methods
• Professional Interface: Clean, intuitive design for efficient calculations

Whether you're a student learning probability theory, a researcher analyzing data, or a professional making statistical decisions, our calculator provides the accuracy and educational value you need for confident probability analysis.

Frequently Asked Questions

Combinations count arrangements where order doesn't matter (nCr), while permutations count arrangements where order does matter (nPr). For example, choosing 3 people from 10 for a committee uses combinations, but arranging 3 people in specific positions uses permutations.
Use the dice roll option in Basic Probability mode. Enter the number of dice and target sum. The calculator determines all possible ways to achieve that sum and divides by total possible outcomes. For example, rolling a sum of 7 with two dice has 6 favorable outcomes out of 36 total possibilities.
Use binomial probability when you have a fixed number of independent trials, each with the same probability of success, and you want to find the probability of exactly k successes. Examples include coin flips, quality control testing, or survey responses where each trial is independent.
Conditional probability P(A|B) is the probability of event A occurring given that event B has already occurred. It's calculated as P(A|B) = P(A ∩ B) / P(B). This is essential for understanding dependent events and is widely used in medical testing, risk analysis, and Bayesian statistics.
Our calculator uses precise mathematical algorithms and handles large factorials efficiently. Results are accurate to multiple decimal places and include proper rounding. For extremely large numbers, the calculator uses logarithmic methods to maintain accuracy while avoiding computational overflow.