Inspired by a Radiolab postcast: what ways are there to compute the probability of observing 7 heads (or 7 tails) in a row when flipping a coin 100 times?
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A:
Each time you start a sequence of 7, there is a 1/(2^7) = 1 in 128 probability that it will be your desired sequence (no matter if its 7 heads/7 tails/something else), and thus a 127 in 128 probability that you will not.
In 100 flips, you can start this sequence 93 times, and in order NOT to hit at least one you need to fail all 93: (127/128)^93 = 48%.
Thus, chance of actually hitting is 100 - 48 = 52%.
truppo
2009-07-06 08:33:18
Shouldn't it be 1/(2^7)*2 if I don't mind if it's heads or tails?Btw, in the meantime I've found this blog post discussing this in more detail: http://www.leancrew.com/all-this/2009/06/stochasticity/
e1i45
2009-07-06 09:54:38