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

[atreic.livejournal.com]

In the interest of supporting people who appear to be right on the internet, I've read the wikipedia page and thought about it, and you appear to be right.

The crux is clearly

From all families with two children, at least one of whom is a boy, a family is chosen at random. This would yield the answer of 1/3.

From all families with two children, one child is selected at random, and the sex of that child is specified. This would yield an answer of 1/2.

You (or nature, or hot velociraptor sex, or the scientist breeding velociraptors, or people who don't understand stats on the internet) have selected a family of two velociraptors at random from the set of all possible families of two velociraptors, and have then acquired the additional information that one velociraptor is a girl. It's clearly the second scenario, not the first. Unless the scientist was producing embryos in some strange probability space where they had to have at least one girl embryo. But if they'd done that they wouldn't need to check them, because they'd know they had at least one girl ;-)

[chuma.livejournal.com]

Bless you :)

I knew someone would put it more succinctly than me. :D

[atreic.livejournal.com]

[In the interests of transparency I think I have to add that I am still managing to confuse myself every time I think about this.]

[atreic.livejournal.com]

I have made an LJ poll to confuse myself further, and friended you so you can read it if you want to and are not entirely sick of this debate already ;-)

[chuma.livejournal.com]

I think theres a section of the thread that already deals with everything that was said here more neatly than it was here, with the outcome that everyone agrees on the appropriate wording required to get the two different percentages (In the section started by Woodpijn). Infact his conclusion on being convinced it was 50% is "I think the boy-girl paradox is as much a linguistic problem as a mathematical one." I entirely agree with him.