Probability Calculator

Turn outcomes into probability. Enter how many outcomes count as success and how many are possible in total — you'll get the probability as a fraction, decimal and percentage, plus the odds and the chance of it not happening.

e.g. 13 hearts in a deck
e.g. 52 cards
Probability of it happening at least once in N tries
Result

How to use this calculator

  1. Count the favorable outcomes — the ways your event can happen.
  2. Count the total possible outcomes — all equally likely results.
  3. Optionally set repeats to see the chance of success at least once over several tries.
  4. Press Calculate for the probability, its complement, and the odds.

Formula used

P(event) = favorable outcomes ÷ total outcomes  ·  P(at least once in n) = 1 − (1 − p)ⁿ

This is classical probability, valid when all outcomes are equally likely. Odds are a ratio of favorable to unfavorable outcomes (13:39 = 1:3), which is different from probability (13/52 = 25%). The at-least-once formula assumes independent tries.

Example calculation

Worked example

Drawing a heart from a deck: 13 favorable / 52 total = 1/4 = 25%. Odds in favor: 13:39 = 1:3.

Drawing at least one heart in 4 draws (with replacement): 1 − 0.75⁴ = 1 − 0.3164 = 68.36% — not 100%, as intuition often suggests.

Probability vs odds — and a common trap

Probability is favorable outcomes divided by all outcomes, running from 0 (impossible) to 1 (certain). Odds compare favorable to unfavorable: a 25% probability is 1:3 odds, not 1:4 — the most common confusion between the two notations.

The other trap is repeated tries: a 25% chance tried four times is not 100%. Failures compound multiplicatively — the chance of missing every time is 0.75⁴ ≈ 32%, so success at least once is only about 68%. That formula, 1 − (1−p)ⁿ, is the honest answer to "if I keep trying, what are my chances?"

Why use this calculator?

Frequently asked questions

What is the difference between probability and odds?

Probability = favorable ÷ total (13/52 = 25%). Odds = favorable : unfavorable (13:39 = 1:3). Bookmakers and gamblers use odds; scientists use probability. Converting: odds of a:b means probability a/(a+b).

If something has a 1 in 10 chance, will it happen in 10 tries?

Not guaranteed — the probability of at least one success in 10 independent tries at p = 0.1 is 1 − 0.9¹⁰ ≈ 65%. There's a 35% chance of ten straight failures. Independent events never "owe" you a success.

How do I calculate the probability of two events both happening?

If they're independent, multiply: P(A and B) = P(A) × P(B). Two coin heads in a row: 0.5 × 0.5 = 25%. If the events affect each other (drawing cards without replacement), the second probability must be updated first.

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