Monty Hall

[andrewducker]

[Poll #1770413]

Explanation

I have known what the answer was for ages, but for some reason it only "clicked" in my head today. You can blame sarahs_muse for triggering it.

Comments

[theweaselking.livejournal.com]

The problem here is the same one you had with Bob and Sue: We're talking about a single specific instance of a larger generalisable problem.

Just because we know Bob won this one game, doesn't mean Bob always wins games, so we can't discount Sue when determining *how often* Bob wins. Just because Sue *can* win games doesn't mean that she might have won this specific game, so we need to take into account that we know she didn't win this one.

Back to the babies: We haven't addressed what might have happened has the first baby been male, because in our specific, that didn't happen.

But we didn't generate raptor pairs guaranteeing one is female.

We generated a random pair of random raptors, and then learned that one, or the other, or both, was female.

The fact that Sue didn't win the game in question doesn't mean that Sue can't win, and thus that Sue's existence doesn't alter the distribution of Bob's wins.

The fact that the Head Scientist determined that one or both of the raptors was definitely female did not change the fact that they *could* have both been male.



You appear to be arguing that by examining only one of them, the head scientist has introduced an ordering to the raptors - the examined and the unexamined......

....and, I think I actually just got what you're aiming at.

Rephrase as "This one is female! The other one escapes and eats you. Was it male or female?" and suddenly the question becomes much clearer.

So you're right, and I do see your point. In the situation where you know which one she examined, it is not the same as "at least one is female".

From the perspective of andrewducker, who owns Jurassic Park 3.0, though, he only knows that the scientist knows one is female without knowing which. If she was to tell him "one is female, argh they've got my neck blergh I am teh dedzorz" all Lovecraft-character-blogging-his-execution-style, though, wouldn't the question of "were both the raptors who ate the scientist female" sit on 33%?

[chuma.livejournal.com]

Deleted my comment as I went off on one without reading the second half of your comment, which I apologise for.

Yes. You got it. By rephrasing it as you have, it is now 33%. Agreed.

[chuma.livejournal.com]

Also with regards to Sue and Bob, I think a better way to phrase it is "Of the times that Bob wins, what proportion will be on his 2nd turn?", which would rule out any ambiguity. I appreciate that this was not YOUR fault as the question was taken as a whole from another forum, but it is misleading none the less.