Binomial Probability Calculator

Ona kuti pane mukana wekuti k zvikwata zvionekwe mu n-zvikwata zvakazvimirira.

P(X = k) —

P(X ≤ k) —

P(X ≥ k) —

Mean (n·p) —

Variance —

Standard deviation —

Zvinyorwa zvinogadziridzwa paunenge uchinyora.

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The binomial probability calculator uses the binomial distribution to model the number of successes in a fixed number of independent trials, each with the same success probability — the classic "how many heads in ten coin flips" problem. It returns the probability of exactly k successes, P(X = k) = C(n, k)·pᵏ·(1 − p)ⁿ⁻ᵏ, along with the cumulative probabilities of at most k and at least k successes.

The term C(n, k) is the number of ways to choose which k of the n trials succeed, pᵏ is the chance those k succeed and (1 − p)ⁿ⁻ᵏ the chance the rest fail. It also reports the distribution’s mean (n·p), variance (n·p·(1 − p)) and standard deviation, and shows the full probability distribution as a table and a chart.

Worked example: for n = 10 flips of a fair coin (p = 50%) the chance of exactly k = 3 heads is C(10, 3) × 0.5³ × 0.5⁷ = 120 × 0.5¹⁰ ≈ 11.7%. The expected number of heads is 10 × 0.5 = 5, with a standard deviation of √(10 × 0.5 × 0.5) ≈ 1.58.

Zvimwe zvinobvunzwa zvakanyanya

Ndiani anogona kushandisa binomial distribution?

Usaishandisa kana paine huwandu hwakasimba hwezvidzidzo zvakazvimirira, chimwe nechimwe chezvidzidzo chinowana zvitatu chete zvezvidzidzo (kubudirira kana kukundikana), uye kubudirira kunogona kuitika nguva nenguva – sekunge uchibata mari 10 nguva kana uchifunga zvinhu zvisina kunaka mubato.

Chii chinonzi chiyero cheP(X = k) uye P(X ≤ k)?

P(X = k) ichokwadi k kubudirira, apo P(X ≤ k) anowedzera kubudirira 0, 1,... kusvika k kubudirira. Kusvika shanduro anobvunza mibvunzo se "izvi ndezvipi kukwanisa kwepakutanga 3 kubudirira?"

Chii chinonzi "n choose k"?

C(n, k), rinoreva "n sarudza k", ndiro rezvimwe nzira dzekuwana kuti k yezvimwe n-zvidzidzo ndezvipi zvinobudirira. Kuti uwane 10 zvidzidzo uye 3 zvidzidzo zvinobudirira, pane C(10, 3) = 120 zvakasiyana-siyana zvezvidzidzo, uye chero chimwe chinowedzera kune iyo yese kufungidzira.

Ndezvipi zvinonzi mean uye standard deviation zvebinomial distribution?

Mutengo (inotarisirwa nhamba yekubudirira) ndeya n·p uye variance ndeya n·p·(1 − p), saka standard deviation ndeya √(n·p·(1 − p)).For 10 fair coin flips the mean is 5 and the standard deviation about 1.58.

Kana ndichigona kufungidzira binomial ne normal distribution?

Kana n iri hombe uye n·p ne n·(1 − p) zviri pamusoro pe10, binomial inonyatso approximate ne normal distribution ine imwe chete mean nestandard deviation.Izvi ndezvimwe zvezvikonzero zvekuongorora zvikamu zvema sampling.

Sei ndinogona kuwana kufungidzira kwe k kubudirira?

P(X ≥ k) inowedzera mukana wekuti k, k+1, … kusvika n kubudirira. Iine 1 − P(X ≤ k − 1), uye iyi binomial probability calculator inotaura zvakananga pamwe chete ne "pazhinji" kunaka.

API — kushandisa iyi kalkulator kubva code

Nhare iyi calculator semahara JSON endpoint - hapana chikuru zvinodiwa. Kutumira nzvimbo mavara pasi separameter query kana JSON. Chii zvachose chaunoisa kunze chinoshandisa default iyo peji iri rakasviba nayo; parameter isiri yechokwadi inonzi 400, uye haisi zero. Tora yakazara API docs →

Endpoint

GET https://calculator.free/api/v1/binomial-probability/

curl

curl "https://calculator.free/api/v1/binomial-probability/?n=10&k=3&p=50"

JavaScript `fetch()`

const r = await fetch(
  "https://calculator.free/api/v1/binomial-probability/?" + new URLSearchParams({
    "n": "10",
    "k": "3",
    "p": "50"
  }));
const data = await r.json();
console.log(data.results);

Zviratidzo zvemubvunzo ndezvekufungidzira kwechinangwa chekudzidzisa chete, kwete zvemari, zvehutano kana zvemari.

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Endpoint

curl

JavaScript fetch()

JavaScript `fetch()`