🚀 go-pugleaf

you, eduardo, and annette are prisoners, and the warden says,
"two of you, chosen at random, are going to be executed tomorrow."
clearly, you have a 1/3 chance of living.  at least one of annette
and eduardo will die, so you ask the warden to tell you the name of
a person, besides yourself, who will be executed.  "annette's gonna
bite it," he says.

now, what's the chance of your survival? it is the chance that eduardo
will be executed, given that annette will be executed.  that is equal
to the chance that both eduardo and annette will be executed, divided
by the chance that annette will be executed.  that's 1/3 divided by
2/3.  that's 1/2.

now you wake up.  your conversation with the warden was a dream.  but,
you think, if i did ask the warden the question, and he did tell me
a name, no matter what name it is, i'd still have a 50/50 chance of
living - so i must have a 50/50 chance anyway!

well, sorry, the fact remains that you did NOT have a conversation, and
the warden did NOT tell you a name.  the only information that you know
is that at least one of eduardo and annette will die.  the chance that
you will live, given that at least one of e. and a. will die, is the
chance that you will live AND at least one of e. and a. will die, divided
by the chance that at least one of e. and a. will die.  that's one third
divided by one.  that's one third.

this is much like the children puzzle - the chance that the other kid is
a girl is different if you know that at least one is a girl than it is
if you know that the younger is a girl.

bob vesterman.