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What is the probability of a coin landing tails 7 times in a row in a series of 150 coin flips?

I was wondering, if you flip a coin 100 times, what is the chance of getting 10 heads or 10 tails in a row? I think this could be a good way to respond to people who think that unlikely things don't happen by chance ( I suspect the chances are over 50%), but I don't know how to do the math.


marked as duplicate by J. M. is a poor mathematician, joriki, Mike Spivey, Asaf Karagila, Hans Lundmark Aug 18 '11 at 20:50

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    $\begingroup$ When people invent a sequence of data, that fact can often be detected from the paucity of runs. Also, if the data are to one decimal place, there will be a paucity of numbers ending in $.0$ and (to a lesser degree) $.5$. But a true scientist would never never invent data. Never. Or at least would be smart enough to use a random number generator. $\endgroup$ – André Nicolas Aug 18 '11 at 19:24
  • $\begingroup$ Probability of a run [1]arxiv.org/abs/math/0511652 $\endgroup$ – Peter Bala Aug 18 '11 at 20:51

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