🚀 go-pugleaf

>From: cooper@cbnewsg.cb.att.com (Ralph 'Hairy' Moonen)

Everything stated is corect, until this:
>   A coin is tossed twice. You are told that *at least* one of the tosses
>   produced heads. What is the probabilty that THE SECOND (and *not* the
>   first!) toss produced heads to make both tosses heads. In this case,
>   the permutations of HT and TH are distinhuished and different. the
>   answer now is 1/3. People read the original question and see the above
>   one, because it's easy to make this mistake. 

What is the prob. that the 2nd toss is heads and not the first, making
both tosses
heads?  Zero!  If the first toss is not heads, then they can't be both heads!
I think you want to re-state this.
I think this is what you mean:

A coin is tossed twice. You know that *at least* one of the tosses is heads.
What is the prob. that the second toss is heads?  Ans = 2/3.
What is the prob. that they are both heads? Ans = 1/3.



The main point with the sibling/coin problem is whether or not the the
probabilities are independent or not.  If you say "One is x, what is the
prob. that the other is also x?", then the probabilities are independent and
the fact that "One is x" doesn't change anything.  If you say "At least
one is x 
(out of two), what is the prob. that number 2 is x?" links the prob.s because
if the first is not-x, then the second _must_ be x, so the answer is different.

Does this sound reasonable?   (I got nailed for missing this on the
first pass :)

Brian /-|-\