Law of Truly Large Numbers

The observation that, across enough opportunities, an event with a small probability can become likely to occur at least once. It is a consequence of repeated trials, not a formal law of probability.

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Complementary probability: The probability that an event does not occur, equal to one minus its probability. The chance of at least one occurrence is easiest to calculate as one minus the chance of none.
Multiple comparisons problem: The increased chance of false positives when many statistical hypotheses are tested. Testing many hypotheses makes at least one spurious result more likely.
Law of large numbers: A theorem stating that sample averages converge toward an expected value as sample size increases. It concerns averages stabilizing, not merely a rare event occurring at least once.
Black swan theory: A framework emphasizing rare, consequential events that are difficult to predict and explain after they occur. It highlights limits of treating all rare events as predictable products of repeated exposure.
Hash collision: An instance in which two distinct inputs produce the same hash value. As more values are hashed, collision probability can rise sharply despite a large output space.
Independence (probability theory): A relationship in which knowing one event occurred does not change the probability of another. For independent trials, the probability of no occurrences multiplies across opportunities.
Look-elsewhere effect: The inflation of apparent statistical significance when many possible patterns or locations are examined. Searching across many possibilities creates more chances for an apparently rare match.
Central limit theorem: A theorem describing how standardized sums of many independent random variables approach a normal distribution. It describes the shape of aggregate fluctuations, rather than the chance of any rare occurrence.
Survivorship bias: A sampling bias caused by focusing on cases that passed a selection process while overlooking those that did not. Visible rare successes can distort judgments about how often repeated attempts succeed.
False positive: A test result indicating a condition is present when it is actually absent. Screening many people can produce numerous false positives even when each test has a low false-positive rate.