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According to Romana II, coincidences were a statistical inevitability, and they were bound to happen sometimes. (AUDIO: Subterranea) The Eleventh Doctor claimed to believe that coincidences were what the universe did for fun. (TV: Closing Time)
Statistically, events on their own would be considered potential coincidences or anomalies until checked against similar examples. (TV: Adrift) Greater degrees of recurrence tended to suggest that apparent anomalies might be connected, and hence were not coincidences. (AUDIO: The Thirteenth Stone)
Some people did not believe in coincidences at all. (TV: The End of Time)
The Eleventh Doctor was known to make discoveries or deductions by paying great attention to apparent coincidences. He reminded himself, "Never ignore a coincidence, unless you're busy. In which case, always ignore a coincidence." (TV: The Pandorica Opens) The Twelfth Doctor followed a similar line of thinking, offering that two variables could either be causally linked or constitute an unlikely coincidence. (TV: The Pilot)
Claims were sometimes made that patterns were mere coincidences in a deliberate attempt to cover up a lie or secret, (TV: Father's Day) even a conspiracy. (TV: Adrift)