some captchas are more difficult than others :)
There's also an official statement as to the rate at which they appear, made by Jeff Atwood on 'How often do captchas appear?' at MSO:
To trigger CAPTCHA while editing /
answering
- The minimum window is 5 seconds
- The maximum window is 40 minutes
There is a maximum of
- one edit every 30 seconds
- one answer every 60 seconds
- one question every 60 seconds
To trigger CAPTCHA while doing
performing other actions, there are
throttles of various sizes depending
on the action -- it's mostly a "slow
down" speed bump to inhibit
potentially dangerous "I'm going to
post obscene things as fast as
possible!" situations.
edit: some new reductions in CAPTCHA
throttle thresholds, if you have >
10k rep:
- for edits -- reduced by two-thirds
- for post submission times -- min seconds reduced by one half, max
minutes increased by x2
edit: assuming you are a logged in
user and have >= 200 reputation: after
successfully completing one captcha,
we now suppress captcha for 5 minutes
on your account.
There's lots of speculation about captchas, like "do captchas get harder/easier over time?", I'm going to boldly attribute all of them to Confirmation Bias. As you rightly point out, this kind of system is basically designed to be wrong very often, so that it can be right when it matters.