> Let me start out in the classical but seemingly
> round about way. Suppose we toss a fair coin 64 times
> recording 0 for tails and 1 for heads. Would either of
> the following two sequences be more surprising?
> (A) 0101010101010101010101010101010101010101010101010101010101010101
> (B) 1101111001110101101101101001101110101101111000101110010100011011
> Actually, I asked this question on talk.origins several years
> ago and many people said something to the effect that while
> they probably would be more surprised to get (A), they shouldn't
> be because both sequences have exactly the same probability of
> occurring. Though this answer is unsettling, it is correct from
> the point of view of classical probability theory.
There is a confusion between probability and predictability. A in the
example,appears rigged, and therefore, not from a fair coin. B in the
example could have been an honest result from tossing a coin. But to
predict the outcome of 64 tosses makes either result equally improbable.
Take another example. Let's assume there are 100,000 tickets issued
to the Super Bowl. The tickets are collected at the gate as the attendees
file in and are set aside in the order in which each person arrived. Should
we expect to get 1 to 100,000 in perfect numerical order. If we got that we
would know with almost total certainty the results were rigged or
non-random. Any sequence showing no obvious pattern, while it COULD
be rigged, at least would look to be what might be expected. So a random
sequence to be truly random, for all practical purposes, should also have
the appearance of being random.
The Origins Solution