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Probability Calculator.

Calculate probability, combinations, permutations, and odds

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01

Set your values

Results update as you type.

Calculated Result

16.67%
Decimal: 0.1667Fraction: 1/6Odds: 1:5

Formula

P(A) = 1 / 6

Steps

  • 1.Identify favorable outcomes: 1
  • 2.Identify total possible outcomes: 6
  • 3.Divide favorable by total: 1 ÷ 6 = 0.1667

FAQs

What is the difference between combinations and permutations?

Combinations count selections where order does not matter, while permutations count arrangements where order matters.

How to Use the Probability Calculator

Calculate the probability of single and combined events.

  1. Enter the number of favorable outcomes.
  2. Enter the total number of possible outcomes.
  3. See the probability as a fraction, decimal, and percentage.

Probability Formulas

Single Event

P(A) = favorable / total

Outcomes you want divided by all equally likely outcomes.

Example:

Input: rolling a 6

Calculation: 1 / 6

Result: ≈ 16.7%

Independent Events (AND)

P(A and B) = P(A) × P(B)

Multiply probabilities of independent events.

Example:

Input: two heads

Calculation: 0.5 × 0.5

Result: 25%

Real-World Use Cases

Games & Odds

Compute dice, card, and lottery odds.

Risk Estimation

Combine event probabilities.

Tips

Tips

  • Probabilities range from 0 (impossible) to 1 (certain).
  • Add for OR (mutually exclusive), multiply for AND (independent).

Cite this calculator

Canonical URL: https://mathify.one/en/math/probability

Cite as: Mathify. (2026). Probability Calculator. https://mathify.one/en/math/probability

Use Cases

Lottery and Game Odds

Determine the odds of winning a lottery or a game by calculating combinations and permutations. For example, find the number of possible 6-number combinations from 49 numbers.

Example: In a 6/49 lottery, the number of combinations is C(49,6) = 13,983,816.

Statistical Analysis and Experiment Design

Calculate probabilities for experiments, surveys, or quality control. Use binomial probability to find the likelihood of a certain number of successes in a sample.

Example: If 10% of products are defective, the probability of exactly 2 defects in a sample of 20 is about 0.285.

Frequently Asked Questions

What is the difference between combinations and permutations?
Combinations (nCr) count the number of ways to choose r items from n items without regard to order. Permutations (nPr) count arrangements where order matters. For example, choosing 3 letters from A, B, C: combinations give 1 (ABC), permutations give 6 (ABC, ACB, BAC, BCA, CAB, CBA).
How do I calculate the probability of multiple independent events?
For independent events, multiply their individual probabilities. For example, the probability of flipping heads (0.5) and rolling a 6 (1/6) is 0.5 × 1/6 ≈ 0.0833. This calculator can handle such calculations for you.
What is binomial probability used for?
Binomial probability calculates the chance of getting exactly k successes in n independent trials, each with the same success probability p. It's used in quality control, surveys, and any scenario with two outcomes (success/failure).

Tips & Common Mistakes

Tips

  • Ensure you understand whether order matters in your problem. If order matters, use permutations; if not, use combinations.
  • For multiple independent events, multiply their probabilities. For mutually exclusive events, add them.
  • When using binomial probability, verify that trials are independent and the success probability is constant.
  • Double-check your inputs for n and r: n must be greater than or equal to r, and both must be non-negative integers.

Common Mistakes to Avoid

  • Confusing combinations and permutations: using nPr when order doesn't matter, or vice versa.
  • Forgetting to convert percentages to decimals when entering probabilities (e.g., 25% should be 0.25).
  • Assuming events are independent when they are not, leading to incorrect probability multiplication.

Last updated: August 13, 2026