Mpikirakira ny mety ho nitranga
Find the probability of k successes in n independent trials.
Manova ny valin'ny fanoratanao.
Momba ity kapila ity
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.
Fanontaniana matetika
Rahoviana no azoko ampiasaina ny fizarana 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.
Inona no fahasamihafana eo amin'ny P(X = k) sy P(X ≤ k)?
Ny P(X = k) dia ny mety ho fahombiazana k, raha P(X ≤ k) dia mampiditra ny mety ho 0, 1,... hatramin'ny k fahombiazana. ny fitambarana ny endrika mamaly fanontaniana toy ny "inona no mety ho fahombiazana 3?"
Inona no "n misafidy k"?
Ny C(n, k), vakio "n misafidy k", dia ny isan'ny fomba samihafa mba hifidy izay k ny n fitsapana dia ny fahombiazana. ho an'ny 10 fitsapana sy 3 fahombiazana dia misy C(10, 3) = 120 toy izany ny fampifangaroana, ary ny tsirairay dia mandray anjara amin'ny mety ho tanteraka.
Inona no atao hoe fizarazarana 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.
Inona no atao hoe fizarazarana ara-dalàna?
Raha ny n dia lehibe sy ny n·p sy ny n·(1 − p) dia farafahakeliny manodidina ny 10, ny binomial dia tsara ny manakaiky ny alalan'ny fizarana mahazatra amin'ny mitovy ny salan'isa sy ny fihemorana ara-dalàna.
Ahoana no ahafahako mahita ny mety ho fahombiazana k farafahakeliny?
Ny P(X ≥ k) dia mampitombo ny mety ho vokatry ny k, k + 1,... hatramin'ny n fahombiazana. izany dia mitovy amin'ny 1 - P(X ≤ k − 1), ary ity binomial mety ho ny calculator mitatitra izany mivantana miaraka amin'ny "ny ambony indrindra" ny sanda.
API — mampiasa io milina fanisana io avy amin'ny rindran'asa
Antsoy ho toy ny farany JSON malalaka ity milina fanisana ity - tsy mila famaha. Mandefa ireo sanda eo amin'ny sehatr'asa etsy ambany ho toy ny mpizaratry ny fanontaniana na JSON. Ny zavatra tsy voalaza dia mampiasa ny sanda tsotra efa nameno ity pejy ity; 400 ny sanda tsy fantatra, tsy aotra tsy misy feo. Vakio ny tahirin-kevitra API feno →
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);Ny voka-pikarohana dia natao ho an'ny torohevitra ankapobeny ihany, tsy torohevitra ara-bola, ara-pitsaboana na ara-bola.