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🎲 Probability Calculator

Calculate the chance of success across multiple tries instantly — enter your single-event probability, number of tries, and a target count k to get four key results in your browser for free.

Each try is independent with the same chance (Bernoulli trials).
At least once
Never (0 times)
Exactly k times
Expected count

About

This probability calculator runs entirely in your browser with no data sent to any server. Enter a single-event probability p (as a percentage), the number of independent trials n, and an integer k. The tool then computes four values using standard probability formulas: P(at least once) = 1 − (1 − p)^n tells you the chance of the event happening one or more times; P(none) = (1 − p)^n gives the chance it never occurs; P(exactly k) uses the binomial formula C(n,k) × p^k × (1 − p)^(n−k) for the precise probability of k successes; and Expected count = n × p shows how many times the event is expected to happen on average. All calculations update instantly as you type.

How to use

  1. Enter the single-event probability as a percentage (e.g. 20 for a 20% chance) in the Probability field.
  2. Enter the number of independent tries n — for example, 10 rolls of a die or 50 coin flips.
  3. Enter k — the exact number of successes you want to evaluate with the binomial formula.
  4. Click Calculate to instantly see P(at least once), P(none), P(exactly k), and expected count — all four results update in real time.
  5. Adjust any input and results refresh automatically — no page reload needed. Results can be copied for use in reports or spreadsheets.

FAQ

What does P(at least once) mean?
It is the probability that the event occurs one or more times across n independent tries, calculated as 1 minus the probability it never happens: 1 − (1 − p)^n.
How is P(exactly k) computed?
The binomial formula is used: C(n,k) × p^k × (1 − p)^(n−k), where C(n,k) is the number of ways to choose k successes from n trials.
What is the expected count and how is it useful?
Expected count = n × p is the average number of times the event will happen over many repetitions. If you flip a 30% coin 10 times, you expect 3 heads on average.
Can I use this for a coin flip or dice roll?
Yes. For a fair coin flip enter p = 50. For rolling a specific face on a six-sided die, enter p ≈ 16.67. Any repeatable event with a fixed per-try probability works.
Is my data sent to a server or stored anywhere?
No. All calculations run in JavaScript directly in your browser. Nothing is transmitted, logged, or stored on any external server.