|The Devil’s Advocate™|
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”.