{"format":2,"method":"deterministic","version":"f3c7c14c3a3f","generated_at":"2026-10-27T14:03:10.337912Z","reason":null,"reason_detail":null,"provenance":"verificada_contra_la_fuente","claims":[{"id":"D1","fact_id":null,"value":50.0,"said_as":"la mitad","text":null,"period":null,"said_in":[{"scene":0,"second":null},{"scene":16,"second":null}],"owner_scene":0,"backing":"ambigua","on_screen":"notShown","citation":null},{"id":"D2","fact_id":"A3","value":23.0,"said_as":"23","text":"Con 23 individuos, el número de pares posibles es 23 × 22 / 2 = 253.","period":null,"said_in":[{"scene":0,"second":null},{"scene":9,"second":null},{"scene":10,"second":null},{"scene":17,"second":null}],"owner_scene":0,"backing":"respaldada_en_su_escena","on_screen":"drawn","citation":{"title":"Birthday problem","url":"https://en.wikipedia.org/wiki/Birthday_problem","doi":null,"as_of":null}},{"id":"D3","fact_id":"A3","value":253.0,"said_as":"253","text":"Con 23 individuos, el número de pares posibles es 23 × 22 / 2 = 253.","period":null,"said_in":[{"scene":0,"second":null},{"scene":10,"second":null},{"scene":17,"second":null}],"owner_scene":0,"backing":"respaldada_en_su_escena","on_screen":"drawn","citation":{"title":"Birthday problem","url":"https://en.wikipedia.org/wiki/Birthday_problem","doi":null,"as_of":null}},{"id":"D4","fact_id":"A12","value":365.0,"said_as":"365","text":"Para simplificar el cálculo, las fuentes descartan los años bisiestos, los mellizos, el sesgo de selección y las variaciones estacionales y semanales en las tasas de natalidad, asumiendo 365 días posibles con igual probabilidad.","period":null,"said_in":[{"scene":1,"second":null},{"scene":14,"second":null}],"owner_scene":1,"backing":"respaldada_en_su_escena","on_screen":"drawn","citation":{"title":"Birthday problem","url":"https://en.wikipedia.org/wiki/Birthday_problem","doi":null,"as_of":null}},{"id":"D5","fact_id":"A17","value":50.0,"said_as":"50 %","text":"Para que al menos una persona en una sala de n personas (excluido uno mismo) comparta cumpleaños con uno en particular, se necesitaría al menos n = 253 personas para superar el 50 % de probabilidad.","period":null,"said_in":[{"scene":3,"second":null}],"owner_scene":3,"backing":"respaldada_en_su_escena","on_screen":"drawn","citation":{"title":"Birthday problem","url":"https://en.wikipedia.org/wiki/Birthday_problem","doi":null,"as_of":null}},{"id":"D6","fact_id":"A17","value":253.0,"said_as":"253","text":"Para que al menos una persona en una sala de n personas (excluido uno mismo) comparta cumpleaños con uno en particular, se necesitaría al menos n = 253 personas para superar el 50 % de probabilidad.","period":null,"said_in":[{"scene":3,"second":null}],"owner_scene":3,"backing":"respaldada_en_su_escena","on_screen":"drawn","citation":{"title":"Birthday problem","url":"https://en.wikipedia.org/wiki/Birthday_problem","doi":null,"as_of":null}},{"id":"D7","fact_id":"A4","value":364.0,"said_as":"364","text":"La probabilidad de que todos los cumpleaños sean distintos en un grupo de n personas es: p̄(n) = 365 × 364 × … × (365 − n + 1) / 365ⁿ.","period":null,"said_in":[{"scene":5,"second":null},{"scene":6,"second":null}],"owner_scene":5,"backing":"respaldada_en_su_escena","on_screen":"drawn","citation":{"title":"Birthday problem","url":"https://en.wikipedia.org/wiki/Birthday_problem","doi":null,"as_of":null}},{"id":"D8","fact_id":"A4","value":365.0,"said_as":"365","text":"La probabilidad de que todos los cumpleaños sean distintos en un grupo de n personas es: p̄(n) = 365 × 364 × … × (365 − n + 1) / 365ⁿ.","period":null,"said_in":[{"scene":5,"second":null},{"scene":6,"second":null}],"owner_scene":5,"backing":"respaldada_en_su_escena","on_screen":"drawn","citation":{"title":"Birthday problem","url":"https://en.wikipedia.org/wiki/Birthday_problem","doi":null,"as_of":null}},{"id":"D9","fact_id":"A4","value":363.0,"said_as":"363","text":"La probabilidad de que todos los cumpleaños sean distintos en un grupo de n personas es: p̄(n) = 365 × 364 × … × (365 − n + 1) / 365ⁿ.","period":null,"said_in":[{"scene":5,"second":null},{"scene":6,"second":null}],"owner_scene":5,"backing":"respaldada_en_su_escena","on_screen":"drawn","citation":{"title":"Birthday problem","url":"https://en.wikipedia.org/wiki/Birthday_problem","doi":null,"as_of":null}},{"id":"D10","fact_id":"A8","value":11.7,"said_as":"11,7 %","text":"Tabla de probabilidades de al menos una coincidencia de cumpleaños según el tamaño del grupo: 5 personas → 2,7 %; 10 personas → 11,7 %; 20 personas → 41,1 %; 23 personas → 50,7 %; 30 personas → 70,6 %; 40 personas → 89,1 %; 50 personas → 97,0 %; 60 personas → 99,4 %; 70 personas → 99,9 %.","period":null,"said_in":[{"scene":7,"second":null}],"owner_scene":7,"backing":"respaldada_en_su_escena","on_screen":"drawn","citation":{"title":"Birthday problem","url":"https://en.wikipedia.org/wiki/Birthday_problem","doi":null,"as_of":null}},{"id":"D11","fact_id":"A8","value":20.0,"said_as":"20","text":"Tabla de probabilidades de al menos una coincidencia de cumpleaños según el tamaño del grupo: 5 personas → 2,7 %; 10 personas → 11,7 %; 20 personas → 41,1 %; 23 personas → 50,7 %; 30 personas → 70,6 %; 40 personas → 89,1 %; 50 personas → 97,0 %; 60 personas → 99,4 %; 70 personas → 99,9 %.","period":null,"said_in":[{"scene":7,"second":null},{"scene":8,"second":null},{"scene":10,"second":null}],"owner_scene":7,"backing":"respaldada_en_su_escena","on_screen":"notShown","citation":{"title":"Birthday problem","url":"https://en.wikipedia.org/wiki/Birthday_problem","doi":null,"as_of":null}},{"id":"D12","fact_id":"A8","value":41.1,"said_as":"41,1 %","text":"Tabla de probabilidades de al menos una coincidencia de cumpleaños según el tamaño del grupo: 5 personas → 2,7 %; 10 personas → 11,7 %; 20 personas → 41,1 %; 23 personas → 50,7 %; 30 personas → 70,6 %; 40 personas → 89,1 %; 50 personas → 97,0 %; 60 personas → 99,4 %; 70 personas → 99,9 %.","period":null,"said_in":[{"scene":7,"second":null},{"scene":8,"second":null}],"owner_scene":7,"backing":"respaldada_en_su_escena","on_screen":"drawn","citation":{"title":"Birthday problem","url":"https://en.wikipedia.org/wiki/Birthday_problem","doi":null,"as_of":null}},{"id":"D13","fact_id":"A8","value":23.0,"said_as":"23","text":"Tabla de probabilidades de al menos una coincidencia de cumpleaños según el tamaño del grupo: 5 personas → 2,7 %; 10 personas → 11,7 %; 20 personas → 41,1 %; 23 personas → 50,7 %; 30 personas → 70,6 %; 40 personas → 89,1 %; 50 personas → 97,0 %; 60 personas → 99,4 %; 70 personas → 99,9 %.","period":null,"said_in":[{"scene":7,"second":null},{"scene":8,"second":null}],"owner_scene":7,"backing":"respaldada_en_su_escena","on_screen":"notShown","citation":{"title":"Birthday problem","url":"https://en.wikipedia.org/wiki/Birthday_problem","doi":null,"as_of":null}},{"id":"D14","fact_id":"A8","value":50.0,"said_as":"la mitad","text":"Tabla de probabilidades de al menos una coincidencia de cumpleaños según el tamaño del grupo: 5 personas → 2,7 %; 10 personas → 11,7 %; 20 personas → 41,1 %; 23 personas → 50,7 %; 30 personas → 70,6 %; 40 personas → 89,1 %; 50 personas → 97,0 %; 60 personas → 99,4 %; 70 personas → 99,9 %.","period":null,"said_in":[{"scene":7,"second":null}],"owner_scene":7,"backing":"respaldada_en_su_escena","on_screen":"drawn","citation":{"title":"Birthday problem","url":"https://en.wikipedia.org/wiki/Birthday_problem","doi":null,"as_of":null}},{"id":"D15","fact_id":"A8","value":50.7,"said_as":"50,7 %","text":"Tabla de probabilidades de al menos una coincidencia de cumpleaños según el tamaño del grupo: 5 personas → 2,7 %; 10 personas → 11,7 %; 20 personas → 41,1 %; 23 personas → 50,7 %; 30 personas → 70,6 %; 40 personas → 89,1 %; 50 personas → 97,0 %; 60 personas → 99,4 %; 70 personas → 99,9 %.","period":null,"said_in":[{"scene":7,"second":null},{"scene":8,"second":null}],"owner_scene":7,"backing":"respaldada_en_su_escena","on_screen":"drawn","citation":{"title":"Birthday problem","url":"https://en.wikipedia.org/wiki/Birthday_problem","doi":null,"as_of":null}},{"id":"D16","fact_id":"A3","value":22.0,"said_as":"22","text":"Con 23 individuos, el número de pares posibles es 23 × 22 / 2 = 253.","period":null,"said_in":[{"scene":10,"second":null}],"owner_scene":10,"backing":"respaldada_en_su_escena","on_screen":"drawn","citation":{"title":"Birthday problem","url":"https://en.wikipedia.org/wiki/Birthday_problem","doi":null,"as_of":null}},{"id":"D17","fact_id":null,"value":190.0,"said_as":"190","text":null,"period":null,"said_in":[{"scene":10,"second":null}],"owner_scene":10,"backing":"sin_respaldo","on_screen":"notShown","citation":null},{"id":"D18","fact_id":null,"value":63.0,"said_as":"63","text":null,"period":null,"said_in":[{"scene":10,"second":null}],"owner_scene":10,"backing":"sin_respaldo","on_screen":"notShown","citation":null},{"id":"D19","fact_id":"A16","value":253.0,"said_as":"253","text":"Con 23 personas, el número de pares (253) es mucho más de la mitad del número de días del año (365).","period":null,"said_in":[{"scene":11,"second":null}],"owner_scene":11,"backing":"derivada","on_screen":"drawn","citation":{"title":"Paradoja del cumpleaños","url":"https://es.wikipedia.org/wiki/Paradoja_del_cumplea%C3%B1os","doi":null,"as_of":null}},{"id":"D20","fact_id":"A16","value":365.0,"said_as":"365","text":"Con 23 personas, el número de pares (253) es mucho más de la mitad del número de días del año (365).","period":null,"said_in":[{"scene":11,"second":null}],"owner_scene":11,"backing":"derivada","on_screen":"drawn","citation":{"title":"Paradoja del cumpleaños","url":"https://es.wikipedia.org/wiki/Paradoja_del_cumplea%C3%B1os","doi":null,"as_of":null}},{"id":"D21","fact_id":"A16","value":50.0,"said_as":"la mitad","text":"Con 23 personas, el número de pares (253) es mucho más de la mitad del número de días del año (365).","period":null,"said_in":[{"scene":11,"second":null}],"owner_scene":11,"backing":"derivada","on_screen":"notShown","citation":{"title":"Paradoja del cumpleaños","url":"https://es.wikipedia.org/wiki/Paradoja_del_cumplea%C3%B1os","doi":null,"as_of":null}},{"id":"D22","fact_id":null,"value":182.0,"said_as":"182","text":null,"period":null,"said_in":[{"scene":11,"second":null}],"owner_scene":11,"backing":"sin_respaldo","on_screen":"notShown","citation":null},{"id":"D23","fact_id":"A6","value":730.0,"said_as":"730","text":"La aproximación exponencial de la probabilidad de al menos una coincidencia es p(n) ≈ 1 − e^(−n(n−1)/730).","period":null,"said_in":[{"scene":12,"second":null}],"owner_scene":12,"backing":"respaldada_en_su_escena","on_screen":"drawn","citation":{"title":"Birthday problem","url":"https://en.wikipedia.org/wiki/Birthday_problem","doi":null,"as_of":null}},{"id":"D24","fact_id":null,"value":365.0,"said_as":"365","text":null,"period":null,"said_in":[{"scene":12,"second":null},{"scene":16,"second":null}],"owner_scene":12,"backing":"ambigua","on_screen":"drawn","citation":null},{"id":"D25","fact_id":"A8","value":30.0,"said_as":"30","text":"Tabla de probabilidades de al menos una coincidencia de cumpleaños según el tamaño del grupo: 5 personas → 2,7 %; 10 personas → 11,7 %; 20 personas → 41,1 %; 23 personas → 50,7 %; 30 personas → 70,6 %; 40 personas → 89,1 %; 50 personas → 97,0 %; 60 personas → 99,4 %; 70 personas → 99,9 %.","period":null,"said_in":[{"scene":13,"second":null}],"owner_scene":13,"backing":"respaldada_en_su_escena","on_screen":"notShown","citation":{"title":"Birthday problem","url":"https://en.wikipedia.org/wiki/Birthday_problem","doi":null,"as_of":null}},{"id":"D26","fact_id":"A8","value":70.6,"said_as":"70,6 %","text":"Tabla de probabilidades de al menos una coincidencia de cumpleaños según el tamaño del grupo: 5 personas → 2,7 %; 10 personas → 11,7 %; 20 personas → 41,1 %; 23 personas → 50,7 %; 30 personas → 70,6 %; 40 personas → 89,1 %; 50 personas → 97,0 %; 60 personas → 99,4 %; 70 personas → 99,9 %.","period":null,"said_in":[{"scene":13,"second":null}],"owner_scene":13,"backing":"respaldada_en_su_escena","on_screen":"drawn","citation":{"title":"Birthday problem","url":"https://en.wikipedia.org/wiki/Birthday_problem","doi":null,"as_of":null}},{"id":"D27","fact_id":"A8","value":70.0,"said_as":"70","text":"Tabla de probabilidades de al menos una coincidencia de cumpleaños según el tamaño del grupo: 5 personas → 2,7 %; 10 personas → 11,7 %; 20 personas → 41,1 %; 23 personas → 50,7 %; 30 personas → 70,6 %; 40 personas → 89,1 %; 50 personas → 97,0 %; 60 personas → 99,4 %; 70 personas → 99,9 %.","period":null,"said_in":[{"scene":13,"second":null}],"owner_scene":13,"backing":"respaldada_en_su_escena","on_screen":"drawn","citation":{"title":"Birthday problem","url":"https://en.wikipedia.org/wiki/Birthday_problem","doi":null,"as_of":null}},{"id":"D28","fact_id":"A8","value":40.0,"said_as":"40","text":"Tabla de probabilidades de al menos una coincidencia de cumpleaños según el tamaño del grupo: 5 personas → 2,7 %; 10 personas → 11,7 %; 20 personas → 41,1 %; 23 personas → 50,7 %; 30 personas → 70,6 %; 40 personas → 89,1 %; 50 personas → 97,0 %; 60 personas → 99,4 %; 70 personas → 99,9 %.","period":null,"said_in":[{"scene":13,"second":null}],"owner_scene":13,"backing":"respaldada_en_su_escena","on_screen":"notShown","citation":{"title":"Birthday problem","url":"https://en.wikipedia.org/wiki/Birthday_problem","doi":null,"as_of":null}},{"id":"D29","fact_id":"A8","value":89.1,"said_as":"89,1 %","text":"Tabla de probabilidades de al menos una coincidencia de cumpleaños según el tamaño del grupo: 5 personas → 2,7 %; 10 personas → 11,7 %; 20 personas → 41,1 %; 23 personas → 50,7 %; 30 personas → 70,6 %; 40 personas → 89,1 %; 50 personas → 97,0 %; 60 personas → 99,4 %; 70 personas → 99,9 %.","period":null,"said_in":[{"scene":13,"second":null}],"owner_scene":13,"backing":"respaldada_en_su_escena","on_screen":"drawn","citation":{"title":"Birthday problem","url":"https://en.wikipedia.org/wiki/Birthday_problem","doi":null,"as_of":null}},{"id":"D30","fact_id":"A8","value":50.0,"said_as":"50","text":"Tabla de probabilidades de al menos una coincidencia de cumpleaños según el tamaño del grupo: 5 personas → 2,7 %; 10 personas → 11,7 %; 20 personas → 41,1 %; 23 personas → 50,7 %; 30 personas → 70,6 %; 40 personas → 89,1 %; 50 personas → 97,0 %; 60 personas → 99,4 %; 70 personas → 99,9 %.","period":null,"said_in":[{"scene":13,"second":null}],"owner_scene":13,"backing":"respaldada_en_su_escena","on_screen":"notShown","citation":{"title":"Birthday problem","url":"https://en.wikipedia.org/wiki/Birthday_problem","doi":null,"as_of":null}},{"id":"D31","fact_id":"A8","value":97.0,"said_as":"97,0 %","text":"Tabla de probabilidades de al menos una coincidencia de cumpleaños según el tamaño del grupo: 5 personas → 2,7 %; 10 personas → 11,7 %; 20 personas → 41,1 %; 23 personas → 50,7 %; 30 personas → 70,6 %; 40 personas → 89,1 %; 50 personas → 97,0 %; 60 personas → 99,4 %; 70 personas → 99,9 %.","period":null,"said_in":[{"scene":13,"second":null}],"owner_scene":13,"backing":"respaldada_en_su_escena","on_screen":"drawn","citation":{"title":"Birthday problem","url":"https://en.wikipedia.org/wiki/Birthday_problem","doi":null,"as_of":null}},{"id":"D32","fact_id":"A8","value":99.9,"said_as":"99,9 %","text":"Tabla de probabilidades de al menos una coincidencia de cumpleaños según el tamaño del grupo: 5 personas → 2,7 %; 10 personas → 11,7 %; 20 personas → 41,1 %; 23 personas → 50,7 %; 30 personas → 70,6 %; 40 personas → 89,1 %; 50 personas → 97,0 %; 60 personas → 99,4 %; 70 personas → 99,9 %.","period":null,"said_in":[{"scene":13,"second":null}],"owner_scene":13,"backing":"respaldada_en_su_escena","on_screen":"drawn","citation":{"title":"Birthday problem","url":"https://en.wikipedia.org/wiki/Birthday_problem","doi":null,"as_of":null}},{"id":"D33","fact_id":"A13","value":50.0,"said_as":"50 %","text":"Los cumpleaños reales no son suficientemente desiguales como para cambiar el resultado: el tamaño de grupo necesario para superar el 50 % de probabilidad de coincidencia sigue siendo 23, igual que en la distribución uniforme teórica.","period":null,"said_in":[{"scene":15,"second":null}],"owner_scene":15,"backing":"respaldada_en_su_escena","on_screen":"drawn","citation":{"title":"Birthday problem","url":"https://en.wikipedia.org/wiki/Birthday_problem","doi":null,"as_of":null}},{"id":"D34","fact_id":"A13","value":23.0,"said_as":"23","text":"Los cumpleaños reales no son suficientemente desiguales como para cambiar el resultado: el tamaño de grupo necesario para superar el 50 % de probabilidad de coincidencia sigue siendo 23, igual que en la distribución uniforme teórica.","period":null,"said_in":[{"scene":15,"second":null}],"owner_scene":15,"backing":"respaldada_en_su_escena","on_screen":"drawn","citation":{"title":"Birthday problem","url":"https://en.wikipedia.org/wiki/Birthday_problem","doi":null,"as_of":null}}],"sources":[{"title":"Birthday problem","url":"https://en.wikipedia.org/wiki/Birthday_problem","doi":null,"authors":[],"role":"principal","read":true,"claims":["D2","D3","D4","D5","D6","D7","D8","D9","D10","D11","D12","D13","D14","D15","D16","D23","D25","D26","D27","D28","D29","D30","D31","D32","D33","D34"]},{"title":"Paradoja del cumpleaños - Wikipedia, la enciclopedia libre","url":"https://es.wikipedia.org/wiki/Paradoja_del_cumplea%C3%B1os","doi":null,"authors":[],"role":"declarada","read":true,"claims":["D19","D20","D21"]}],"summary":{"codex":"present","figures_total":34,"backed_in_scene":26,"derived":3,"unbacked":3,"context_only":0,"figures_on_screen":{"drawn":24,"approx":0,"withheld":0,"notShown":10},"plotted_values_approx":0,"plotted_values_withheld":0,"figures_outside_the_cut":0},"doi":null,"certifications":[],"claimsDigest":"c873e6ae3555a9a4fd30997d51f0977f640b7dcb406d72518b16141d9951053c"}