Probability Calculator

Classical, hypergeometric and at-least-once probability

Quick Answer

Probability Calculator: Classical, hypergeometric and at-least-once probability. Classical: P = favorable ÷ total equally-likely outcomes.

p per try

Tries

P(at least once in 100 tries)

63.3968%

All miss36.6032%

Tries for 50%69

Tries for 90%230

Tries for 99%459

Steps (complement rule)

1P(all miss) = (1−p)^n = (1−0.01)^100
2P(至少中一次) = 1 − (1−0.01)^100 = 0.6340
3Tries for target q: n = ln(1−q) / ln(1−p)

Everyday probabilities

Scenario	Probability
3 heads in a row	12.5%
Roll a 6 (one die)	16.67%
Sum of 7 (two dice)	16.67%
1% pull, ≥1 in 10 pulls	9.56%
1% pull, ≥1 in 100 pulls	63.4%
CN lottery jackpot (approx)	1 / 17,721,088

💡 Gambler's fallacy: independent trials have no memory — after 10 heads, the next flip is still 50/50. But the 'at least once' probability of repeated trials grows fast: 1%×100 pulls is 63.4%, not 100%.

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How to Use

Enter values or expressions: type directly into the Probability Calculator — keyboard friendly.
Instant results: everything computes live as you type, no button needed.
Follow the steps: the result panel shows full working and formula substitution.
Copy or recompute: one-click copy; change any input to recalculate instantly.

Key Points

Probability Calculator is a free online math tool — open and use, no sign-up.
All calculations run locally in your browser; your data never leaves the device.
Key capability: Classical, hypergeometric and at-least-once probability.
Results come with formulas and reference tables so you can verify every number.

Formula & How It Works

Three probability models

Classical: P = favorable ÷ total equally-likely outcomes

Hypergeometric (no replacement): P = C(M,X)·C(N−M,K−X) ÷ C(N,K)

At least once (independent trials): P = 1 − (1−p)ⁿ

Example: single-trial 10%, 5 trials → at least one success = 1−0.9⁵ = 40.95%.

FAQ

How do I use the Probability Calculator?

Open the page and fill in the input fields — results update automatically. Classical, hypergeometric and at-least-once probability.

Are the results accurate?

Yes. All calculations use standard mathematical formulas and are verified for accuracy.

Is it free? Do I need to sign up?

Completely free. No registration, login or download required — just open and use.

Does it work on mobile?

Yes. The responsive design works on phones, tablets and desktops.

Is my data saved?

No. All calculations run locally in your browser. Nothing is uploaded or stored.

Related Guides

Source & Updates

Standard mathematical formulas. All logic verified. Last updated: 2025-07

Last updated: 2026-08-04

Formulas and content on this page are reviewed by the YiJianSuan team. For reference only — official sources prevail.

Cite this page: YiJianSuan. Probability Calculator[EB/OL]. https://www.yijiansuan.com/en/c/math/probability

Results provided by this tool are for reference only and do not constitute professional advice.