Probability Calculator Suite

Calculate probabilities, combinations, permutations, binomial, and conditional probability

Calculate simple probabilities and set operations
Number of successful outcomes
Total possible outcomes

Visual Probability Representation

Enter values to see probability visualization

Understanding Probability

Basic Probability

The probability of an event is the ratio of favorable outcomes to total possible outcomes.

P(Event) = Favorable Outcomes / Total Outcomes

Combinations vs Permutations

Combinations (nCr)

Order doesn't matter

Example: Selecting 3 people from 10 for a committee

Permutations (nPr)

Order matters

Example: Arranging 3 people in specific positions

Binomial Probability

Used when you have a fixed number of independent trials, each with the same probability of success.

  • Each trial has only two outcomes (success or failure)
  • Trials are independent
  • Probability of success is constant
  • Number of trials is fixed

Real-World Examples

Dice Rolling

Basic probability: 1/6 chance for any number on a fair die

Lottery

Combinations: Choosing 6 numbers from 49 = C(49,6)

Coin Flips

Binomial: Getting exactly 6 heads in 10 flips