Kifaa cha Kupima Ukubwa wa Uzazi

Pata uwezekano wa mafanikio ya katika hali ya kutopata majaribu.

%
P ngumuX = k) —
P ngumuX ▿ k) —
P ngumuX ▿ k) —
Neno (n·p) —
Zoea —
Kukengeuka —

Matokeo yanakuwa bora zaidi unapochapa.

Je, hesabu hiyo ilikupa jibu linalofaa?

Kuhusu kifaa hiki cha kupigia hesabu

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.

Maswali yaliyoulizwa mara nyingi

Ninaweza kutumia lini kugawanywa kwa mali?

Itumie wakati kuna majaribio fulani ya kujitegemea, kila kesi ina matokeo mawili tu (mafanikio au kutofaulu), na uwezekano wa kufanikiwa ni uleule kila wakati tokapo kwa kutupilia mbali sarafu mara 10 au kuhesabu vitu vyenye kasoro katika fungu.

Kuna tofauti gani kati ya P MiddleX = k) na P ngumuX ngumu)?

P(X = k) is the chance of exactly k successes, while P(X ≤ k) adds up the chances of 0, 1, … up to k successes. The cumulative version answers questions like "what is the probability of at most 3 successes?"

"kinachagua k" ni nini?

CClinton, k), husomwa "n choice k", ni idadi ya njia tofauti za kuchagua ni zipi ke majaribu ni mafanikio. Kwa ajili ya majaribu 10 na mafanikio 3 kuna Ctoka10, 3) = michanganyo 120 kama hiyo, na kila moja huchangia uwezekano kamili.

Ni nini maana na ugeugeu wa kiwango cha kutosambaa kwa mali?

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.

Ninaweza kukadiria lini mali hizo na ugawanyaji wa kawaida?

When n is large and both n·p and n·(1 − p) are at least about 10, the binomial is well approximated by a normal distribution with the same mean and standard deviation. This is the basis of many large-sample proportion tests.

Ninapataje uwezekano wa angalau mafanikio ya k k?

P(X ≥ k) sums the probabilities of k, k+1, … up to n successes. It equals 1 − P(X ≤ k − 1), and this binomial probability calculator reports it directly alongside the "at most" value.

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API bustanini hutumia kifaa hiki cha hesabu kutoka kwenye mfumo wa sheria

Ipigie simu kifaa hiki cha kupigia hesabu kama Junse É not doot toder. Chochote unachoacha kinatumia kiwango kilekile cha mwisho ambacho ukurasa huu haujakamilika; parameta isiyojulikana ni 400, si sufuri kimya kamwe. Soma habari kamili za API docs →

keyboard label

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);

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