Probability calculator with steps — independent, conditional, and combinatorics

Step-by-step examples: compute independent event probabilities, a worked conditional probability example, and combinatorics (combinations/permutations) with numbers.

Tool

Use the main Probability Calculator for interactive calculations: Open probability calculator.

Examples

  1. Independent events: coin toss
    1. Problem: Probability of two heads in two fair coin tosses.
    2. P(heads) = 1/2, so P(heads twice) = 1/2 * 1/2 = 1/4 = 0.25
    3. Answer: 0.25
  2. Conditional probability (cards)
    Problem: What is P(ace | red)? In a 52-card deck there are 26 red cards and 2 red aces.
    1. P(ace ∩ red) = 2/52 = 1/26
    2. P(red) = 26/52 = 1/2
    3. P(ace | red) = P(ace ∩ red) / P(red) = (1/26) / (1/2) = 2/26 = 1/13 ≈ 0.0769
    4. Answer: 1/13 ≈ 0.0769
  3. Combinations vs permutations
    Problem: Choose 3 people from 10 (order doesn't matter) and order 3 people from 10 (order matters)
    1. Combinations: C(10,3) = 10! / (3! 7!) = 120
    2. Permutations: P(10,3) = 10 * 9 * 8 = 720
    3. Answer: Combinations = 120, Permutations = 720