Coin flip: Difference between revisions
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{{a| | {{a|stats|}}Per {{author|Nassim Nicholas Taleb}}’s {{br|The Black Swan: The Impact of the Highly Improbable}} You have a coin which, on the last 99 flips, had come up heads. Assume it is a fair coin. What is the probability of it coming up tails on the 100th flip? | ||
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The odds of a fair coin landing heads 99 times in a row is 0.5 * 10<sup>99</sup>, which is just shy of half a googol. If it takes ten minutes to flip a coin 100 times, it is likely to happen once in a period of several gazillion times the estimated life of the universe. So, the odds of a ''fair'' coin landing heads is, of course, 0.5. The odds that a coin which lands heads 99 times in a row *is fair* is as close to zero as doesn’t matter. | The odds of a fair coin landing heads 99 times in a row is 0.5 * 10<sup>99</sup>, which is just shy of half a googol. If it takes ten minutes to flip a coin 100 times, it is likely to happen once in a period of several gazillion times the estimated life of the universe. So, the odds of a ''fair'' coin landing heads is, of course, 0.5. The odds that a coin which lands heads 99 times in a row *is fair* is as close to zero as doesn’t matter. | ||
Latest revision as of 09:13, 26 June 2024
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Lies, Damn Lies and Statistics
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Per Nassim Nicholas Taleb’s The Black Swan: The Impact of the Highly Improbable You have a coin which, on the last 99 flips, had come up heads. Assume it is a fair coin. What is the probability of it coming up tails on the 100th flip?
The odds of a fair coin landing heads 99 times in a row is 0.5 * 1099, which is just shy of half a googol. If it takes ten minutes to flip a coin 100 times, it is likely to happen once in a period of several gazillion times the estimated life of the universe. So, the odds of a fair coin landing heads is, of course, 0.5. The odds that a coin which lands heads 99 times in a row *is fair* is as close to zero as doesn’t matter.
Lesson: don’t trust assumptions. They make an “ass” out of “u” and —“mptions”.