Mueen Nawaz <m.n### [at] ieeeorg> wrote:
>         2) The monkey problem is isomorphic to this one: If I have an unbiased
> coin (and assume the outcome _is_ random, and not related to chaos -
> such as the force I hit it with, etc), and I keep flipping it, is it
> possible that I can get a continuous string of heads indefinitely?

>         Intuition tells me yes. I just can't see any physical reason why I
> _have_ to get a tails at some point.

>         Yet _every_ single person - mathematician, probabilist, or otherwise
> says the answer is no because the probability of such an event happening
> is 0 in the limit to infinity. If you do 1 minus that, you get  that the
> probability of a tails appearing at _some_ point is 1. In fact, you're
> the _first_ person I've seen who has the same dilemma with this problem
> as I do.

  I'd say that the probability being 1 with infinite throws is exactly as
meaningful as the probability of getting a certain value of a continuous
range being 0. Yes, it's mathematically zero, but that doesn't mean that
the value will never be chosen (if it meant that, it would mean that no
value would *ever* be chosen because all the individual values have a
probability of zero).

  Likewise the probability of getting tails being 1 with infinite throws
doesn't really tell us that tails must appear at some point. After all,
you *can't* throw a coin an infinite amount of times, and even the idea
has no correspondence to any physical event. It's a purely mathematical
construct. What the 1 tells as is that it's the upper limit for the
probability.

  I'd think about it this way: No matter how many times you throw, there's
*always* a non-zero probability that it will be all heads. At no point is
tails *forced* to appear by any law of nature or mathematics. (This is
because past tosses do not affect future ones.)

-- 
                                                          - Warp

Post a reply to this message