[nnoitra]

You are really confused about this. In general a randomly generated sequence on average will have equal 1s and 0s. Try generating 100K sequences and then count the sequences with:

1) equal 1s and 0s

2) all 1s

3) all 0s

See which one is more likely.

[icambron]

You missed the parent’s point. “Equal 1s and 0s” is not a sequence; it’s a class of sequences. So the fact that sequences with that property are more common than the specific sequence “all 1s” is true but doesn’t answer the question. 11110000 is a different sequence than 10101010. The question this thread is exploring is whether 1111111 is more likely than any other sequence, e.g. than 1111000 in particular (or insert any other sequence). And of course the answer is no.

[danparsonson]

The point the parent is making is that 1) represents a class of results rather than a single result, and any single member of that class is equally as likely as 2) or 3). Obviously the class as a whole is more likely than any other single result, but that's a different assertion.

[skykooler]

I believe what pessimizer means is that while "all 1s" is not as likely as "equal 1s and 0s", it is just as likely as any individual string of 1s and 0s - for example, 111111 is just as likely as 100110.