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Probability Calculator

Math Calculators

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(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)

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

Everyday probabilities

ScenarioProbability
3 heads in a row12.5%
Roll a 6 (one die)16.67%
Sum of 7 (two dice)16.67%
1% pull, ≥1 in 10 pulls9.56%
1% pull, ≥1 in 100 pulls63.4%
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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  1. Enter values or expressions: type directly into the Probability Calculator — keyboard friendly.
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  3. Follow the steps: the result panel shows full working and formula substitution.
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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?
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Source & Updates

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

Last updated:

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

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