Research any topic before you write.

Find related topics. | Discover entities. | See connections. | Build a topical map.

Birthday problem

In probability theory, the birthday problem asks for the probability that, in a set of n randomly chosen people, at least two will share the same birthday. The birthday paradox is the counterintuitive fact that only 23 people are needed for that probability to exceed 50%.

Calculating the probability, Other birthday problems & Generalizations

Use the mouse wheel or two fingers (on touchscreens) to zoom in and out of the map.

Research this topic

Explore the main themes, entities and connections around Birthday problem. Start with the topic map, then use the sections below for research and deeper semantic analysis.

Explore this topic

Start with a few of the strongest sections from the source topic. These are research directions, not a list of keywords you must use.

Topics to explore

Browse the full topic structure. Each item opens a new analysis centered on that subject.

Overview

Calculating the probability

Approximations

An upper bound on the probability and a lower bound on the number of people

Generalizations

Other birthday problems

Partition problem

In fiction

Bibliography

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

Map overview Semantic statistics

Birthday problem

Nodes82
Edges81
Triples102
Avg. degree1.98
Density0.02439
Components1

How this topic connects Entity context

See the strongest relationship patterns around the current topic before diving into the raw triples.

Birthday problem

Top relations

related to Bibliography · 49
Birthday problem → Abramson, Abused, American Mathematical Monthly, Basic Books, Blinder, Bloom, Chemistry, Colmez, Coralie, Courtroom, Diana Sylvester, Elsevier, Engineering Students, Essential Math, Finite Mathematics, First, Frederick, Frederick Mosteller, Generalized Birthday Problem, Gerald
related to External links · 16
Birthday problem → Archived, Better Explained, Birthday Probability, Brady Haran, Computing, EduMaterials, Eric, Eurobirthdays, Grime, James, MathWorld, Numberphile, Retrieved, The Birthday Paradox, Wayback MachineUnderstanding, WolframAlpha
related to Average number of people to get at least one shared birthday · 8
Birthday problem → Computer Programming, Donald Knuth, If, In, It, Pr, The, The Art
related to In fiction · 8
Birthday problem → Arthur, As, Clarke's, Eventually, Fall, If, May, Moondust
related to Arbitrary number of days · 5
Birthday problem → A033810, Given, In, OEIS, The
related to Number of people until every birthday is achieved · 5
Birthday problem → Coupon, For, Hn, It, The
related to Calculating the probability · 4
Birthday problem → An, JavaScript, The, With
related to Everyone shares a birthday · 4
Birthday problem → A380129, For, OEIS, The
related to Same birthday as you · 2
Birthday problem → By, In
related to Probability of a shared birthday (collision) · 1
Birthday problem → The

Important terminology Word statistics

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

birthday people probability number problem two 23 365 least one birthdays days 50 first group displaystyle given shared person event

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Birthday problemrelated to Arbitrary number of daysGiven0.60section
Birthday problemrelated to Arbitrary number of daysIn0.60section
Birthday problemrelated to Arbitrary number of daysThe0.60section
Birthday problemrelated to Arbitrary number of daysA0338100.60section
Birthday problemrelated to Arbitrary number of daysOEIS0.60section
Birthday problemrelated to Average number of people to get at least one shared birthdayIn0.60section
Birthday problemrelated to Average number of people to get at least one shared birthdayIf0.60section
Birthday problemrelated to Average number of people to get at least one shared birthdayPr0.60section
Birthday problemrelated to Average number of people to get at least one shared birthdayThe0.60section
Birthday problemrelated to Average number of people to get at least one shared birthdayDonald Knuth0.60section
Birthday problemrelated to Average number of people to get at least one shared birthdayThe Art0.60section
Birthday problemrelated to Average number of people to get at least one shared birthdayComputer Programming0.60section

Related concept clusters Concept neighborhoods

These clusters group vocabulary that occurs around closely connected concepts in the source material.

    Connections between topic areas Semantic bridges

    Bridges can reveal useful research angles that are easy to miss in a flat list of related terms.

    Min side: 3
    For writers, content strategists, SEOs, marketers and creators — from quick topic research to advanced semantic analysis.