HERC777 wrote: > I knew it was around 20 since 2^20 = 1048576 > > say there are 1048576 flippers. > each has 1 / 1048576 chance of matching up to 20. > > a million people, each has 1 in a million chance, odds are (on average) > someone will score. > ---------------------------------------
That wasn't your original question. Your original question was, on average, would one of these flippers' sequences MATCH YOUR sequence. Matching YOUR sequence MEANS matching your sequence to 100 places, not 20. The probability of THAT is negligible. On average, that DOESN'T HAPPEN, period.
If, instead of having a million people flip coins 100 times, you have them flip *20* times, then, "on average", yes, one of the million flippers will match you all 20 times. The probability is 1/e that none of them matches, and another 1/e that exactly one of them matches, and (e-2)/e that two or more of them match you. There is a ridiculously tiny (but still positive and bigger than epsilon) probability that all million of them match you. To get the expected or "average" number of flippers matching, you have to multiply each of these numbers-of-flippers by the probability of actually having that number match you, and it winds up summing to 1. 1/e or 36.8% of the time, it is 1 to begin with. But the 36.8% of the time that it is 0 is balanced out by the 26.4% of the time that it is 2 or greater.