{"uid":"cap_1xUOAC2cDiBFjXXbFNLjX","slug":"binomial-distribution-calculator-828c53be","name":"Binomial Distribution Calculator","description":"Binomial distribution with `trials` (n ≥ 0, ≤ 1e6) and success `probability` (0..1). `function` selects the mass (pmf), cumulative distribution (cdf) or quantile / inverse-CDF.","url":"https://distribution.openverbs.com/v1/binomial","method":"POST","headers":{},"bodySchema":{"type":"object","$schema":"https://json-schema.org/draft/2020-12/schema","required":["input"],"properties":{"input":{"type":"object","required":["type","method","bodyType","body"],"properties":{"body":{"type":"object","required":["function","x","trials","probability"],"properties":{"x":{"type":"number","description":"Number of successes k (integer for pmf) for pmf/cdf, or the probability p ∈ (0,1) for quantile."},"trials":{"type":"integer","maximum":1000000,"minimum":0,"description":"Number of trials n."},"function":{"enum":["pmf","cdf","quantile"],"type":"string"},"probability":{"type":"number","maximum":1,"minimum":0,"description":"Success probability per trial."}},"additionalProperties":false},"type":{"type":"string","const":"http"},"method":{"enum":["POST"],"type":"string"},"bodyType":{"enum":["json","form-data","text"],"type":"string"}},"additionalProperties":false}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.004","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.004/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.004","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.004","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_zXHPqOqi0TeJ3gFOjaGze","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.004","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes PMF, CDF, or quantile values for the binomial probability distribution given trial count, success probability, and number of successes.","exampleAgentPrompt":"What's the probability of getting exactly 7 successes out of 20 trials if the success probability per trial is 0.4? Use the PMF function.","exampleUseCases":[{"title":"Coin flip probability check","prompt":"If I flip a fair coin 15 times, what's the probability of getting exactly 8 heads? Use the binomial PMF."},{"title":"Quality control defect modeling","prompt":"In a production batch of 500 items where each item has a 2% defect rate, what's the cumulative probability that 12 or fewer items are defective? Use the binomial CDF."},{"title":"A/B test success threshold","prompt":"For an A/B test with 100 trials and a 35% baseline conversion rate, what's the 95th percentile quantile of the binomial distribution? Use the quantile function."}],"resultDescription":"Returns a numeric probability or quantile value corresponding to the requested binomial distribution function (PMF gives P(X=k), CDF gives P(X≤k), quantile gives the smallest k such that CDF(k) ≥ p).","failureModes":["Invalid function enum value (not pmf, cdf, or quantile) returns a validation error","x out of range for given trials causes a computation error","probability not in [0,1] range returns a 400-level error","trials exceeding maximum of 1,000,000 triggers a schema validation rejection","malformed body structure returns an input parsing error"],"whenToPreferThis":"Choose this endpoint when you need fast, on-demand computation of binomial distribution statistics (PMF, CDF, or quantile) without standing up your own math library or statistical computing environment. Ideal for agents performing probabilistic reasoning, quality control modeling, or statistical hypothesis testing as part of a larger workflow.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-15T00:31:39.057Z","isFirstParty":false}