If you take an information theory point of view, then a single question could provide more than a single bit of information, but it never will on average (for s

If you take an information theory point of view, then a single question could provide more than a single bit of information, but it never will on average (for some suitable meaning of "average"). If I'm speaking to 1 of 1024 possible people and I ask "Are this particular woman?" then 1 time out of 1024 I will learn 10 bits of information, but 1023 out of 1024 times I will learn approximately zero bits of information.