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.

Nezve iyi kalkulator

the binomial distribution is used to calculate 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. 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.The binomial probability calculator uses the binomial distribution to model the number of successes in aWorked exampleWorked example: for n = 10 flips of a fair coin (p = 50%) the chance of exactly k = 3 heads is C(n, k) × 0.5³ × 0.5⁷ ≈ 11.7%. The expected number of heads isTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWorked exampleTheWork

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 zvinobudirira, pane C(10, 3) = 120 zvakasiyana-siyana zvezvidzidzo, uye chimwe nechimwe 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 "pakutanga" kunaka.

API — kushandisa iyi kalkulator kubva code

Chiva iyi calculator semahara JSON endpoint - hapana chikuru zvinodiwa. Kutumira nzvimbo zviwanikwa pasi separameter query kana JSON. 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.

Nezve iyi kalkulator

Zvimwe zvinobvunzwa zvakanyanya

Maitiro ekuita Calculators

Endpoint

curl

JavaScript fetch()

JavaScript `fetch()`