Probability
A number between 0 and 1 expressing how likely an event is, and the branch of mathematics that studies such measures. It is the basis for quantifying uncertainty in statistics, physics, and finance.
Get 23 people together and the odds two share a birthday already top 50%. With 365 days, you might expect far more, but the question is not "who matches me" — it is "do any two match." Among 23 there are 253 possible pairs. At 70 people, the probability hits 99.9%: the birthday paradox.
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Two games that each guarantee a loss can become a winning strategy when played alternately. One game's result influences the other's conditions, allowing you to selectively hit favorable outcomes. This is known as 'Parrondo's paradox.'
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The 'Sleeping Beauty problem' is a famous probability paradox. If a coin lands heads, she is woken once; if tails, twice with memory erased. The 'Halfer' camp says heads is 1/2, the 'Thirder' camp says 1/3, and both answers are logically valid.
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To perfectly randomize a deck of cards, a riffle shuffle needs just 7 repetitions, while the overhand (Hindu) shuffle requires about 10,000.
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If a disaster has a 0.1% chance and a 99%-accurate alarm is installed, out of ~110 alarm days in 10,000, about 100 are false alarms. Over 90% are wrong—yet dismissing the alarm means ignoring a 99%-accurate warning. This is the "base rate fallacy," where probability defies intuition.
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