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]

I actually do see your argument now, yes.

I still think you're *wrong*, but now I understand where you're coming from

The problem here is that you're not supposed to know which coin you looked at - only that examination of the coins has shown that one is heads.

You, instead, are aiming to exclude all cases where the first coin examined is tails, which *would* result in 50/50 - except we're not discussing that. Not even in the original question, where I phrased it poorly and implied a possible ordering to the raptors.

Instead, the original phrasing, corrected and clarified three hours ago, was meant to imply that examination of a random raptor from the pair had resulted in a female, and the second raptor had not yet been examined.

Which, given our original four equally likely possibilities of
MM
MF
FM
FF
Means we're SOMEWHERE in the bottom three, but we don't know which.
We have either FX or XF, and in 2/3 of the possible cases X is M.

[chuma.livejournal.com]

ARGH!

Thats STILL 50%

The point is the 33% comes from being able to look at BOTH of them and say that at least one is female!

If you look at the first one and it is female you can say with certainty "at least one is a female" whether or not you look at the second, which happens 50% of the time. The point is that if you see the first one is male then you can STILL look at the second one and if that is female you can STILL say "at least one is a female", which happens 25% of the time.

In THAT scenario it is 33% that both are female. Only identifying ONE of them without looking at the other means that you CANNOT assume ANYTHING OTHER THAN the one she looked at IS female. That means the other one is the ONLY unknown and therefore it is a 50-50.

The key to phrasing this is that a female can be either or both rather than a specific one.

Please PLEASE try and understand this. Read your own link again and then maybe we can agree and move on.

[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.