Probability Calculator

Calculate combinations, permutations, and probability of events

Probability Formulas

Combinations (nCr)

nCr = n! / (r! × (n-r)!)

Where n is total items and r is items chosen

Permutations (nPr)

nPr = n! / (n-r)!

Where n is total items and r is items arranged

Basic Probability

P(A) = (Favorable Outcomes) / (Total Outcomes)

Conditional Probability

P(A|B) = P(A ∩ B) / P(B)

Benefits & Features

Our probability calculator offers multiple advantages:

Comprehensive Probability Tools

  • Combinations and Permutations
  • Basic Probability Calculations
  • Conditional Probability
  • Binomial Probability
  • Step-by-step Solutions

Educational Features

  • Clear Formula Explanations
  • Detailed Step-by-step Solutions
  • Visual Learning Aids
  • Practice Problems
  • Real-world Examples

User-Friendly Interface

  • Easy Input Selection
  • Clear Result Display
  • Multiple Calculation Types
  • Mobile-friendly Design
  • Instant Calculations

Frequently Asked Questions

Combinations (nCr) represent the number of ways to select items where order doesn't matter. Permutations (nPr) represent the number of ways to arrange items where order does matter. For example, selecting 2 cards from a deck is a combination, while arranging 2 cards in a specific order is a permutation.

Conditional probability P(A|B) is the probability of event A occurring given that event B has occurred. It's calculated as P(A|B) = P(A ∩ B) / P(B), where P(A ∩ B) is the probability of both events occurring and P(B) is the probability of event B.

Binomial probability calculates the probability of exactly k successes in n independent trials, where each trial has the same probability p of success. The formula is P(X = k) = C(n,k) × p^k × (1-p)^(n-k), where C(n,k) is the number of combinations.

To convert a decimal probability to a percentage, multiply by 100. For example, a probability of 0.25 is 25%. To convert from percentage to decimal, divide by 100. For example, 75% is 0.75 probability.