Binomial Probability Calculator
Chọta ihe oyiyi nke k n'ime n n'ime
Nhọrọ ndị ahụ ga-akpụzi mgbe ị na-etipụta.
N'ihe banyere calculator a
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.
Ajụjụ ndị a na-ajụkarị
Kedụ mgbe m ga-eji binomial distribution?
Jiri ya mgbe e nwere ọnụọgụgụ ahọpụtara nke nnyocha ọbụla, nnyocha ọbụla nwere ihe n'ime ya abụọ (nrụpụta ma ọ bụ mmehie), na nrụpụta ọbụla bụ otu mgbe ọbụla - dị ka ịkpụgharị ego 10 ugboro ma ọ bụ ịgụta ihenhọrọ na-adịghị mma n'ime batch.
Gịnị bụ ọdịiche dị n'etiti P(X = k) na P(X ≤ k)?
P(X = k) bụ ohere nke n'ezie k n'atọlitela, ebe P(X ≤ k) na-agbakwunye n'elu ohere nke 0, 1,... ruo n'atọlitela k. Nsụgharị n'ime ya na-aza ajụjụ dị ka "gịnị bụ ohere nke n'ọtụtụ 3 n'atọlitela?"
Gịnị bụ "n họrọ k"?
C(n, k), read "n choose k", is the number of different ways to pick which k of the n trials are the successes. For 10 trials and 3 successes there are C(10, 3) = 120 such combinations, and each contributes to the total probability.
Gịnị bụ n'etiti na ịdị n'otu n'ihi ntụgharị nke binomial distribution?
Oge (ọnụọgụgụ nke nrụpụta a na-atụ anya) bụ n·p na varians bụ n·p·(1 − p), ya mere, ụkpụrụ deviation bụ √(n·p·(1 − p)). Maka 10 n'obere bụ 5 na ụkpụrụ deviation bụ 1.58.
Kedụ ka m ga-esi kọwaa binomial na n'ozuzu ya?
Mgbe n bụ nnukwu na n·p na n·(1 − p) bụ n'okpuru 10, binomial bụ nke a na-ahazi nke ọma site na nkịtị n'ịgwakọta na n'otu n'otu na standard deviation. Nke a bụ n'okpuru nke ọtụtụ nnyocha n'ihe gbasara n'ozuzu.
Olee otú m ga-esi hụ na ọbụla k n'ime ihe ndị ahụ ga-eme?
P(X ≥ k) na-agbakwunye n'ihe n'eme nke k, k+1,... ruo n'ihe n'eme. Ọ dị otua na 1 − P(X ≤ k − 1), na binomial n'eme nke a na-egosipụta ya n'ụzọ ziri ezi n'akụkụ "n'ọtụtụ" valiu.
API — jiri kaadị a site na kóòdù
Kpọọ kalkulata a dịka ebe ngwụcha JSON n'efu - enweghị kii achọrọ. Ziga valiu ebe ahụ n'okpuru dịka paramita ajụjụ mọọbụ JSON. Ihe ọbụla ị na-ewepụ na-eji dìfọ́ọ̀ltụ̀ nke a na-edebe ihuakwụkwọ a na ya; parameter a na-amaghị bụ 400, ọ dịghị sẽọ̀rọ̀. Gụọ ngwe ndị ahụ niile →
Ebemkpofuozi
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);Ihe a na-ahụta bụ n'ihi nlekọta n'ozuzu ya, ọ bụghị nlekọta ego, ọgwụ ma ọ bụ nlekọta ego.