"birthday problem" meaning in English

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  "lang_code": "en",
  "pos": "noun",
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      "glosses": [
        "The mathematics problem that concerns the probability there exist two people in a random group who share a birthday."
      ],
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          "probability theory",
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          "mathematics",
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          "birthday",
          "birthday"
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      "raw_glosses": [
        "(probability theory) The mathematics problem that concerns the probability there exist two people in a random group who share a birthday."
      ],
      "related": [
        {
          "word": "birthday paradox"
        }
      ],
      "topics": [
        "mathematics",
        "probability-theory",
        "sciences"
      ],
      "translations": [
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "mathematical observation",
          "word": "syntymäpäiväparadoksi"
        },
        {
          "code": "de",
          "lang": "German",
          "sense": "mathematical observation",
          "tags": [
            "neuter"
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          "word": "Geburtstagsparadoxon"
        }
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        "birthday problem"
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  "word": "birthday problem"
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  "lang_code": "en",
  "pos": "noun",
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      "word": "birthday paradox"
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        "The mathematics problem that concerns the probability there exist two people in a random group who share a birthday."
      ],
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          "mathematics",
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        "(probability theory) The mathematics problem that concerns the probability there exist two people in a random group who share a birthday."
      ],
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        "mathematics",
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        "sciences"
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  "translations": [
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "mathematical observation",
      "word": "syntymäpäiväparadoksi"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "mathematical observation",
      "tags": [
        "neuter"
      ],
      "word": "Geburtstagsparadoxon"
    }
  ],
  "word": "birthday problem"
}