{"uid":"cap_sW5gFOET8AWq1zUa_xA7x","slug":"birthday-problem-probability-calculator-3aa92eee","name":"Birthday Problem Probability Calculator","description":"Birthday problem: chance two people in a group share a birthday, chance someone shares yours, group size for 50 or 99 percent.","url":"https://probability-calc.x402tookit.com/birthday-problem?utm_source=zero.xyz","method":"GET","headers":{},"bodySchema":{"type":"object","$schema":"https://json-schema.org/draft/2020-12/schema","required":["input"],"properties":{"input":{"type":"object","required":["type","method"],"properties":{"type":{"type":"string","const":"http"},"method":{"enum":["GET"],"type":"string"},"queryParams":{"type":"object","required":["people"],"properties":{"days":{"type":"integer","description":"Equally likely birthdays (default 365)"},"people":{"type":"integer","description":"Group size, 1 to 100000"}}}},"additionalProperties":false},"output":{"type":"object","required":["type"],"properties":{"type":{"type":"string"},"example":{"type":"object","properties":{"asOf":{"type":["null","string"]},"days":{"type":["null","number"]},"people":{"type":["null","number"]},"source":{"type":["null","string"]},"reasons":{"type":["array","null"],"items":{"type":"string"}},"summary":{"type":["null","string"]},"verdict":{"type":["null","string"]},"degraded":{"type":["boolean","null"]},"disclaimer":{"type":["null","string"]},"notChecked":{"type":["array","null"],"items":{"type":"string"}},"expectedSharedPairs":{"type":["null","number"]},"probabilityAnyShared":{"type":["null","number"]},"peopleForFiftyPercent":{"type":["null","number"]},"probabilityNoneShared":{"type":["null","number"]},"peopleForNinetyNinePercent":{"type":["null","number"]},"probabilitySomeoneSharesYours":{"type":["null","number"]},"peopleForFiftyPercentSharingYours":{"type":["null","number"]},"othersNeededForFiftyPercentSharingYours":{"type":["null","number"]}}}}}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.02","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":"$0.02/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.02","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.02","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_dx99E_MKqPyzscmw2yjhJ","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.02","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Calculates birthday problem probabilities: chance any two people in a group share a birthday, chance someone shares your birthday, and group sizes needed for 50% or 99% probability thresholds.","exampleAgentPrompt":"What's the probability that at least two people in a group of 30 share a birthday? Also tell me how many people you'd need for a 50% and 99% chance of a match.","exampleUseCases":[{"title":"Classroom birthday paradox demo","prompt":"I'm teaching a class of 28 students and want to know the probability that at least two of them share a birthday — can you run the birthday problem calculation for a group of 28?"},{"title":"Party planning birthday odds check","prompt":"I'm throwing a party with 50 people. What's the chance that at least two guests share a birthday, and what are the odds someone shares my specific birthday?"},{"title":"Finding the 50% threshold for birthday match","prompt":"How many people need to be in a room before there's at least a 50% chance that two of them share a birthday? Also give me the number for a 99% chance."}],"resultDescription":"Returns a JSON object containing: probability that at least one pair shares a birthday, probability that no one shares a birthday, probability that someone shares your specific birthday, the expected number of shared pairs, and the minimum group sizes needed to reach 50% and 99% chance of any shared birthday, plus the group size needed for a 50% chance someone shares your birthday. Also includes metadata fields like source, asOf, and any disclaimers.","failureModes":["Missing required 'people' query parameter returns an error","People value outside range 1–100000 may return an error or unexpected result","Non-integer values for 'people' or 'days' may be rejected","Very large group sizes may produce probabilities indistinguishable from 1.0","Payment failure returns HTTP 402 before computation occurs"],"whenToPreferThis":"Use this endpoint when you need precise birthday problem probability computations — especially the classic paradox scenario (chance any pair shares a birthday), the personalized variant (chance someone shares YOUR birthday), or the threshold group sizes for 50%/99% confidence. Prefer this over a general statistics API when the birthday problem is the specific question, as it returns all relevant variants in a single call with clean structured output.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-10-29T13:13:45.276Z","isFirstParty":false,"canonicalSlug":"birthday-problem-probability-calculator-3aa92eee"}