Àwọn

Wá àwọn ìṣàmúlò-ètò tí a lè gbà nínú àwọn ìṣàmúlò-ètò aládàrẹ̀.

P(X = k) —

P(X ≤ k) —

P(X ≥ k) —

Àwọn ìṣàmúlò-ètò —

Àwọn ìṣàfarawé —

Àwọn ìṣàmúlò-ètò —

Àwọn Àtòjọ-ẹ̀yàn àwọn ìṣàmúlò-ètò

Ńlà àwọn àwọn ààtò àtòjọ-ẹ̀yàn yìí?

Àkóónú ìṣàmúlò-ètò yìí

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.

Àwọn Àtòjọ-ẹ̀yàn

Njẹ́ mò lè ló àwọn ìṣàfarawé àwọn ìṣàmúlò-ètò binomial?

Use it when there is a fixed number of independent trials, each trial has just two outcomes (success or failure), and the success probability is the same every time — like flipping a coin 10 times or counting defective items in a batch.

Kini iyatọ laarin P(X = k) ati P(X ≤ k)?

P(X = k) ní ìpèwọ̀n tí a tì fi àwọn ìṣẹ̀dá k ṣé, nígbà tí P(X ≤ k) tí n fi àwọn ìpèwọ̀n tí a tì fi 0, 1,... lọ́wọ́lọ́wọ́. Àwọn ìṣàfarawégbèsì tí a tì fi àwọn ààyè bí "wọn nìyìn àwọn ìpèwọ̀n tí a tì fi àwọn ìṣẹ̀dá 3 lọ́wọ́lọ́wọ́ lọ́wọ́lọ́wọ́?"

Kini "n yan k"?

C(n, k), ka "n yan k", ní àwọn ìrísí-lẹ́tà àwọn ìṣàmúlò-ètò tí a lò láti yan àwọn k tí a tí n gbiyanju ní àwọn ìṣẹ̀dá. Fun àwọn 10 àwọn 3 ìṣẹ̀dá ní C(10, 3) = 120 àwọn ìṣàmúlò-ètò bẹ̀rẹ̀, àti gbogbo wọn ní àwọn ìṣàmúlò-ètò.

Kini àwọn ìṣàmúlò-ètò àti àwọn ìṣàmúlò-ètò ìṣàfarawé àwọn ìṣàmúlò-ètò 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.

Njẹ́ mò lè fi àwọn àwọn ìṣàmúlò-ètò àwọn ìṣàmúlò-ètò àwọn ìṣàmúlò-ètò pamọ́?

Ti n bá jẹ́ nla, ti n·p ati n·(1 − p) bá jẹ́ nípa 10, binomial tí a fi pọ̀ jú lọ́wọ́lọ́wọ́ nípa ìparípọ̀ ìṣàfarawe-ẹ̀yàn nípa aago kan atí ìdàdé. O jẹ́ ìrísí-lẹ́tà tí a lò fún àwọn ìṣàmúlò-ètò ìbára-ẹ̀yàn nla.

Bawo ni mo ṣe lè rí ìgbàgbọ́ tí a bá fẹ́ k-ìdáràn?

P(X ≥ k) fi àwọn ìṣàmúlò-ètò tí k, k+1,... lọ́wọ́lọ́wọ́. O jẹ́ ìwọ̀n 1 − P(X ≤ k − 1), àti àwọn ìṣàmúlò-ètò ìṣàmúlò-ètò binomial yìí ń sọ̀rọ̀ ní pàtó nínú "àwọn ohun tí o ju" àwọn fálù.

API — ló àwọn ìṣàmúlò-ètò yìí láti inú ìṣàmúlò-ètò

Fi àwọn ìṣàmúlò-ètò yìí kọ̀ǹpútà yìí láti jẹ́ ààyè-iṣẹ́ JSON tí a tí fi pamọ́ - kò ní bọ́tìnì kan tí a fẹ́. Fi àwọn fálù ààyè-iṣẹ́ sílẹ̀ sí bí àwọn àwọn ìṣàmúlò-ètò àti JSON. Anything you omit uses the same default this page is pre-filled with; an unknown parameter is a 400, never a silent zero. Ka àwọn àkọlé API kíkún →

Àwọn Ààyè Ìjánu-ìṣàmúlò-ètò

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.

Àkóónú ìṣàmúlò-ètò yìí

Àwọn Àtòjọ-ẹ̀yàn

Àwọn Ìṣàmúlò-ètò Ìṣàmúlò-ètò

Àwọn Ààyè Ìjánu-ìṣàmúlò-ètò

curl

JavaScript fetch()

JavaScript `fetch()`