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bonanova · Daedalian Member

Ned, Red, Ted and Zed are identical quadruplets, alike in every way except one:
the way that they describe the children in families that have two children.

1. Ned says one is a boy, if that is a true statement; otherwise he says one is a girl.
2. Red says one is a girl, if that is a true statement; otherwise he says one is a boy.
3. If the older child is a boy, Ted says one is a boy; otherwise he says one is a girl.
4. Zed flips a coin and considers the taller (heads) or shorter (tails) child.
If the coin-selected child is a boy, he says one is a boy; otherwise he mentions the sex of the other child.

One of the four men, we don't know which, then tells us:

"So there is this family with two kids. One of them is a girl."

What is the probability that the other child is a girl?

Assume the usual 50% birth numbers and a family chosen at random from a statistically neutral population.
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Duke Gnome · Daedalian Member

[0.5714?
37.5% of instances will be someone other than Zed, saying "girl"
6.25% of instances will be Zed saying "girl"

25% of all instances will be someone saying girl and the other kid being a girl
25/43.75=57.14%]

Trojan Horse · Daedalian Member

Bah. I should've visited this site last night.

I agree with Duke Gnome.

Zag · Unintentionally offensive old coot

I disagree with DG (and TH)

Before we heard anything, there were sixteen cases with equal probability. Here's a chart of what that person would say in each of the four possible arrangements of the family in question.

Sorry, code sections don't "spoiler."

Trojan Horse · Daedalian Member

I disagree with your conclusions about Zed, Zag.

If the family has one girl and one boy, then Zed will always say that the family has a boy. If the coin-selected child is the boy, then Zed will say that the family has a boy. If the coin-selected child is the girl, then Zed will mention the sex of the other child: namely, a boy.

Zag · Unintentionally offensive old coot

Sure enough, I misread Zed's algorithm. I'll start again and see if I now come up with the same answer DG did

In looking at it, I realize that Zed's rule is the same as Ned's. He only says 'Girl' if both children are girls, no matter what he flips.

(1) Zed's coin selection chooses the first-mentioned child
(2) Zed's coin selection chooses the second-mentioned child