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Think you understand Monty Hall? Try the Tuesday boy problem.

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Re: Think you understand Monty Hall? Try the Tuesday boy problem.

#31

Post by fuzzix »

ars wrote: post #3

I hate this one because while it says: "I have two children and one is a son born on a Tuesday." It actually means: "I have two children and only one of them is a son born on a Tuesday." You are supposed to just assume this modification.

"I have two children and one is a son born on a Tuesday."

If it were about the phrasing you could assume the other child is a daughter - if he were to continue ... "The other is also a son, born on a Friday" it would just sound strange.

Perhaps it is all down to his turn of phrase :)

Re: Think you understand Monty Hall? Try the Tuesday boy problem.

#32

Post by incremental »

twelvechairs wrote: post #19
incremental wrote: post #16

Earlier quoted context omitted.

Since the constraint simply says that at least one child is a boy, we don't need to distinguish between two types of BB. This is a curious misconception, by the way. The typical failure mode I see on these questions is people having difficulty accepting BG and GB as different possibilities.

If we are determined to look at order of birth (ie. have a BG and GB) then we should consider all cases by order of birth, so where 'B' represents the boy we know and 'b' or 'g' represents a child we dont, and the first character represents the first child, and the second the second childe - we have: Bb, bB, Bg, gB 50%.

Imagine a similar problem but with red and blue poker chips. Say, for example, that I have a bag and I pull out two chips, one at a time.

In this problem, would you still try to distinguish the two identical red poker chips using your logic?

Re: Think you understand Monty Hall? Try the Tuesday boy problem.

#33

Post by tallanvor »

nadam wrote: post #21

As the currently top voted comment does not get it, I try to intuitively explain the paradox. No, it is not ambiguity of language. It says formally: I have two children. There exists a child of mine who is (boy and born on tuesday). And yes, the probability of the other child being a boy is 13/27. To understand this, try a more extreme case: When a child is born we generate a random number: rnd(1billion) Now the man…

Well, you're talking about probabilities being greater than 1... That doesn't really make sense in this discussion.

Re: Think you understand Monty Hall? Try the Tuesday boy problem.

#34

Post by losvedir »

user24 wrote: post #2

Doesn't this rest on the simple ambiguity in the phrasing? > I have two children and one is a son born on a Tuesday. If by that is meant: > I have two children. Here is some information about one of them: son, born on Tuesday. Then the probability of the other child being a son is 1/2. If on the other hand we mean: > I have two children. One or more is a son. Exactly one of them was born on a Tuesday. Then we get the…

Yeah, I was very confused what exactly the "paradox" was at first, too, and why the expected interpretation should be the one it was. Here's how I finally see it:

If I say, "I have two cars, one's a 1994 Porsche 911", then I think it's reasonable to interpret that statement to mean the other car is not also a '1994 Porsche 911', but doesn't speak at all to its Porsche-ness, 1994-ness, or 911-ness. Rather, I'm wrapping them all up in a package, and saying the other is not this exact combination of characteristics.

Similarly, if I say, "I have two children. One's a son born on Tuesday," I think I now understand that I'd probably interpret that to mean the other child is not a son born on Tuesday. It doesn't speak to the gender or day of birth beyond that.

With that knowledge, that the other child is not a (son AND Tuesday-born), that's when the 13/27 arises.

Re: Think you understand Monty Hall? Try the Tuesday boy problem.

#35

Post by rimantas »

rubergly wrote: post #8

Let's try a simpler problem. Suppose we know that a certain man has two children and we also know that the older one is a boy. In this case we would say that the probability that the other child is a boy is 1/2. After all, the sex of one child is independent of the sex of the other child. That the older child is a boy has no bearing on the sex of the younger child. Now suppose we know simply that a man has two childr…

  > Why is time so special?
Because it is a part of the condition? How else can you have "older child" in your condition, if time is not important? Stating that first child is a boy is the same as opening the door in Monty Hall problem: it eliminates particular combination.

If you don't know the order of the kids you have three ways to have a situation where two boys are possible: BB, BG, GB. When you know that first one is a boy, you eliminate the GB case and are only left with BB and BG.

Re: Think you understand Monty Hall? Try the Tuesday boy problem.

#37

Post by dmd »

tallanvor wrote: post #33
nadam wrote: post #21

As the currently top voted comment does not get it, I try to intuitively explain the paradox. No, it is not ambiguity of language. It says formally: I have two children. There exists a child of mine who is (boy and born on tuesday). And yes, the probability of the other child being a boy is 13/27. To understand this, try a more extreme case: When a child is born we generate a random number: rnd(1billion) Now the man…

Well, you're talking about probabilities being greater than 1... That doesn't really make sense in this discussion.

I think it's fairly clear that nadam means 1/2, not 2.

Re: Think you understand Monty Hall? Try the Tuesday boy problem.

#38

Post by nadam »

ars wrote: post #27
nadam wrote: post #25

Earlier quoted context omitted.

The other can also be born on Tuesday. (generated id = 1 in rnd(7)) And the other can also have a generated id = 456783123 in rnd(1billion). But as the bound of the rnd is bigger and bigger, the probability of that approaches to zero. So as we know more and more information of one of the children, we are closer and closer to simply uniquely identifying him, so the probability of the other being a boy approaches 2.

If both can be born on Tuesday then telling me one was born on Tuesday does not uniquely identify him! It's not unique if both can do it. And since it's not unique the rest of your analysis is based on a faulty assumption. (BTW I did not downmod you, in case you were wondering.)

It is about specifying a child, and then saying it is a boy.

The one extreme is: one of my children is a boy. in this case the other is a boy with 1/3 probability.

The other extreme is: One of my children has a national unique id=... He is a boy. The other is a boy with 1/2 probability.

And other cases are in between. The more information you provide on the first child (the less chance there is that the other can have the same property, the more close you are to 1/2.

Of course in the rnd(7) example we are in-between:

1/3 < 13/27 < 1/2

Re: Think you understand Monty Hall? Try the Tuesday boy problem.

#39

Post by user24 »

losvedir wrote: post #34
user24 wrote: post #2

Doesn't this rest on the simple ambiguity in the phrasing? > I have two children and one is a son born on a Tuesday. If by that is meant: > I have two children. Here is some information about one of them: son, born on Tuesday. Then the probability of the other child being a son is 1/2. If on the other hand we mean: > I have two children. One or more is a son. Exactly one of them was born on a Tuesday. Then we get the…

Yeah, I was very confused what exactly the "paradox" was at first, too, and why the expected interpretation should be the one it was. Here's how I finally see it: If I say, "I have two cars, one's a 1994 Porsche 911", then I think it's reasonable to interpret that statement to mean the other car is not also a '1994 Porsche 911', but doesn't speak at all to its Porsche-ness, 1994-ness, or 911-ness. Rather, I'm wrappin…

> that the other child is not a (son AND Tuesday-born), that's when the 13/27 arises.

No. The other can be (son AND Tuesday-born) as well and the probability is still 13/27. See Colin's reply to me.

Re: Think you understand Monty Hall? Try the Tuesday boy problem.

#40

Post by user24 »

dmd wrote: post #37
tallanvor wrote: post #33

Earlier quoted context omitted.

Well, you're talking about probabilities being greater than 1... That doesn't really make sense in this discussion.

I think it's fairly clear that nadam means 1/2, not 2.

it is now he's edited it. Wasn't clear before, to me at least. But then I "don't get it" so what do I know ;)

edit: can't reply to you as HN isn't giving me the option. But: No worries, I didn't take it personally, just a little dig :)

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