I-Calculator ye-Binomal Probability

Fumana ukwenzeka kwempumelelo ye k kwi n izifundo ezizimeleyo.

%
P( X = k) —
P(X ≤ k) —
P( X ≥ k) —
Ixabiso eliphakathi (n· p) —
Utshintsho —
Ithambeka Elisezantsi —

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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.

Imibuzo ebuza rhoqo

Ndisebenzisa njani unikezelo lwe-binomial?

Sebenzisa xa kukho inani elimiselweyo leentlanganiso ezizimeleyo, iintlanganiso nganye zineempawu ezimbini kuphela (uphumelela okanye ukungaphumelelanga), kwaye ukwenzeka kwempumelelo kufanayo ngazo zonke iimeko - njengokujikelezisa imali yegolide amaxesha angama-10 okanye ubalo lwezinto ezibi kwiqela.

Yintoni utshintsho phakathi kweP(X = k) neP(X ≤ k)?

P(X = k) yingozi yempumelelo epheleleyo ye k, ngelixa iP(X ≤ k) idibanisa ingozi ye0, 1, … ukuya kwimpumelelo ye k. Uhlobo oludityanisiweyo luphendula imibuzo njenge "luthini ukwenzeka kwempumelelo eninzi ye 3?"

Yintoni "n khetha k"?

C( n, k), funda "n khetha k", yinani leendlela ezahlukeneyo zokukhetha k ye n iimvavanyo eziphumelelayo. Kwiimvavanyo ezili-10 ne3 eziphumelelayo kukho i C( 10, 3) = 120 ezidityanisiweyo, kwaye nganye ixhasa ukwenzeka okupheleleyo.

Yintoni i-mean kunye ne-standard deviation yonikezelo lwe-binomial?

The mean (expected number of successes) is n·p and the variance is n·p·(1 − p), so the standard deviation is √(n·p·(1 − p)). For 10 fair coin flips the mean is 5 and the standard deviation about 1.58.

Ndizakuba ndikwazi nini ukuthelekiswa kwe-binomial ngonikezelo oluqhelekileyo?

Xa i n ikhulu kwaye zombini i n· p ne n· (1 − p) zimalunga ne 10, ibininomial ilungelelaniswe kakuhle ngokunikezelwa okuqhelekileyo ngenye iphakathi kunye nokuguquka okuqhelekileyo. Oku kuyinkxaso yovavanyo oluninzi lwemilinganiselo yesampuli enkulu.

Ndiyifumana njani inyaniso ye k izigqibo eziphumelelayo?

P(X ≥ k) idibanisa iimfuno ze k, k+1,... ukuya kwi n mpumelelo. Ilingana ne 1 - P(X ≤ k - 1), kwaye le calculator ye binomial imfuno ixela ngokuthe ngqo ecaleni kwe "ixabiso elikhulu".

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Nceda le khadi lemali njengendawo esemva ye-JSON ekhululekileyo - akukho qhosha lifunekayo. Thumela amaxabiso endawo ezantsi njengeparameter yombuzo okanye i-JSON. Nantoni na oyenzayo isebenzisa okungagqibekanga okufanayo eli phepha ligqityiwe ngaphambili; iparameter engaziwayo yi 400, ayikho i zero ekhululekileyo. Funda i-API epheleleyo →

Incopho yesiphelo

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);

Results are estimates for general guidance only, not financial, medical or tax advice.