"birthday paradox" meaning in English

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      "expansion": "birthday paradox",
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
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          "name": "Probability theory",
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      ],
      "glosses": [
        "The counterintuitive observation that a random group of people needs to have only 23 members before there is a 50% chance of two of them having the same birthday."
      ],
      "id": "en-birthday_paradox-en-noun-HD515~v4",
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          "probability theory",
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        [
          "counterintuitive",
          "counterintuitive"
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          "random",
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        [
          "chance",
          "chance"
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      ],
      "raw_glosses": [
        "(probability theory) The counterintuitive observation that a random group of people needs to have only 23 members before there is a 50% chance of two of them having the same birthday."
      ],
      "related": [
        {
          "word": "birthday problem"
        }
      ],
      "topics": [
        "mathematics",
        "probability-theory",
        "sciences"
      ],
      "translations": [
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "mathematical observation",
          "word": "syntymäpäiväparadoksi"
        },
        {
          "code": "de",
          "lang": "German",
          "sense": "mathematical observation",
          "tags": [
            "neuter"
          ],
          "word": "Geburtstagsparadoxon"
        },
        {
          "code": "pt",
          "lang": "Portuguese",
          "sense": "mathematical observation",
          "tags": [
            "masculine"
          ],
          "word": "paradoxo do aniversário"
        }
      ],
      "wikipedia": [
        "birthday paradox"
      ]
    }
  ],
  "word": "birthday paradox"
}

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      "expansion": "birthday paradox",
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "birthday problem"
    }
  ],
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        "en:Probability theory"
      ],
      "glosses": [
        "The counterintuitive observation that a random group of people needs to have only 23 members before there is a 50% chance of two of them having the same birthday."
      ],
      "links": [
        [
          "probability theory",
          "probability theory"
        ],
        [
          "counterintuitive",
          "counterintuitive"
        ],
        [
          "random",
          "random"
        ],
        [
          "chance",
          "chance"
        ]
      ],
      "raw_glosses": [
        "(probability theory) The counterintuitive observation that a random group of people needs to have only 23 members before there is a 50% chance of two of them having the same birthday."
      ],
      "topics": [
        "mathematics",
        "probability-theory",
        "sciences"
      ],
      "wikipedia": [
        "birthday paradox"
      ]
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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"
    },
    {
      "code": "pt",
      "lang": "Portuguese",
      "sense": "mathematical observation",
      "tags": [
        "masculine"
      ],
      "word": "paradoxo do aniversário"
    }
  ],
  "word": "birthday paradox"
}