I mean N1, of course. Fairly unlikely, I'll admit.
Speaking of which, ss Joseph and I should conclude this probability discussion.
At this point I'm entirely sure that I'm right, but want to convince you. I might have to dedicate a thread to it tomorrow.
Right now, bed.
right, I had written a post about that which I then didn't submit because faust said no
But I saved it, and can post it now.
Here is your post for context, and
here is the example I'm referencing.
And if you still want to know the actual flaw in your argument - well, not every outcome you or I are listing is in fact equally likely. It would be equally likely if we had zero information about the flips, but since we know that heads has been flipped 9 times, this particular out:
HTHHHHHHHH
is much less likely than this
HHHHHHHHHH
because, if heads has been flipped 9+ of 10 times, then each individual flip is much more likely to
have been heads, and therefore the second flip is much more likely to have been heads.
basically, it's the difference between 'what's the chance for 9 heads in 10 flips vs 10 heads?' (10-1) or 'we already flipped 9 heads; what's the chance that the tenth is also a head vs that it's a tails? (1-1)
You said you simulated it. What you simulated is probably "what's the odds of 2 P's and 1 K out of 3 letters looking only at those who have 2K's?' or something to that effect, thus making the same mistake as you did above.
What you should simulate is, you randomly set two letters to the results we already know, and randomize a result for the third one. Except then it is so simple that you don't need to simulate it anymore, because you can effectively take out the letters which you have already determined, and only have to look at one.
I know the feeling of getting your mind wrapped around such a problem and getting really confused with it, it happened to me before. It proves that you have an urge to understand stuff on a deep level. But in this case the result is just really simple.