I have a son born on xDay. What is the probability that my next kid will be a son?
I dont get Monty Hall :(
Think you understand Monty Hall? Try the Tuesday boy problem.
91–100 of 152 posts
Re: Think you understand Monty Hall? Try the Tuesday boy problem.
#92I've been thinking about this for an hour, and I'm now convinced that the author is wrong. The fact that we found out about one of the children from the father means that all probabilities are not equal, even though they're treated here like they are. The difference is between the information being offered, and determined independantly. I'll do this with the boy/girl problem, for simplicities sake. If we ask a man if…
The issue here is with assumptions - you have made a different set of assumptions from the author, and hence are getting a different result. A lot of people here are having similar issues, by misreading exactly what the initial proposition means. Your reasoning above relies on the 'likeliness' of a man giving you the information, which is something that is not meant to be a part of the problem. Although it is phrased…
I agree that that is what the author intended to communicate. But I actually think that's a bigger stretch than my own interpretation - it changes how the information was determined, which has a definite impact on the outcome.
The reason why I posted was to suggest that the author should have worded it the second way, i.e.
A man has two children, and one is a son born on a Tuesday. What is the probability that the other child is also a son?
Which leaves no doubt. I guess I didn't really make that clear enough with my original post.
Re: Think you understand Monty Hall? Try the Tuesday boy problem.
#93Earlier quoted context omitted.
We can assume he's selecting one of his children at random, and revealing their birthday and gender. This is the entire point of the article, IMO: we have to make some assumption about how we selected this guy to talk to, and how he chose what to tell us. It's not pinned down by the statement of the problem, and what you might consider a natural assumption is not necessarily what other people might assume. Which is w…
I definitely agree - I hate problems like this, because the difficulty is caused by ambiguity of English, not the problem itself. But even given other assumptions as to why the father selects the child he does - sort by date, males first etc, the author's answer of 13/27 is still almost certainly wrong - he should have just taken the father out of the equation completely.
I agreee -- this problem should not be discussed in English. Python seems better: http://news.ycombinator.com/item?id=3290313
Re: Think you understand Monty Hall? Try the Tuesday boy problem.
#94Earlier quoted context omitted.
No, it is not ambiguity of language. This is a big call to make, seeing as English is not your native language. As a native English speaker, I find it very ambiguous as to which set of probabilities I should be counting.
I meant that the paradoxical nature is not resolved by simply formalizing the statement into first order logic the following way: "I have 2 children. Exists child where (Born_on_tuesday(child) and Boy(child))." (Some other paradoxes completely disappear when you try to write the statement into first order logic. It is not the case here.) This is what I wanted to say.
You see, the problem is that even your latest attempt to describe the question is ambiguous - the solution depends on how 'I' was selected. And if ever you describe that in a non-ambiguous manner, I suspect that the answer would no longer seem paradoxial. In other words, ambiguity in language is at the very heart of this problem.
Re: Think you understand Monty Hall? Try the Tuesday boy problem.
#95Earlier quoted context omitted.
We can assume he's selecting one of his children at random, and revealing their birthday and gender. This is the entire point of the article, IMO: we have to make some assumption about how we selected this guy to talk to, and how he chose what to tell us. It's not pinned down by the statement of the problem, and what you might consider a natural assumption is not necessarily what other people might assume. Which is w…
I definitely agree - I hate problems like this, because the difficulty is caused by ambiguity of English, not the problem itself. But even given other assumptions as to why the father selects the child he does - sort by date, males first etc, the author's answer of 13/27 is still almost certainly wrong - he should have just taken the father out of the equation completely.
I don't think this has anything to do with the ambiguity of language or English. It does, however, like the Monty Hall problem, require you to make assumptions about how/why a speaker presents certain information.
Think of it like this. What would the father say if he did in fact have two boys who were both born on Tuesday. Would he really say, "I have two children and one is a son born on a Tuesday"? Wouldn't he instead say, "I have two children and both are sons born on a Tuesday."?
I mean he could say it the first way, but such a comment would be borderline misleading. To say you have one son born on Tuesday when in fact you have two is technically correct, but I think the problem assumes that the man is speaking somewhat plainly.
So I do agree with you that communication intent is ambiguous, but I agree with some others that this is sort of the whole point of the problem, and it's not always immediately obvious that statistical information is hiding in seemingly irrelevant data.
Re: Think you understand Monty Hall? Try the Tuesday boy problem.
#96Earlier quoted context omitted.
Alternatively, suppose we label the combinations of child-day BM, GM, BT, GT ... BU, GU (14 items). We have a bucket with 2 of each of these combinations, as there are 2 kids (total 28 items). The problem states that we have taken one "BT" item out of the bucket (so 27 items left), and are asking how many "B*" items are left in the bucket (13). The confusion arises because one can consider the same problem with repla…
What would the question have to be to make the following the answer? Suppose we label the combinations of child-day BM, GM, BT, GT ... BU, GU (14 items). We have two buckets which both contain a copy of each combination (total 28, 14 in each bucket). The problem states that we have taken one "BT" item out of one bucket, and are asking how many "B " items are left in the other bucket (7 out of 14).
That would be two parents having one child each, one of whom says his only son was born tuesday, and asking what 's the probability the other guy has a son.
Re: Think you understand Monty Hall? Try the Tuesday boy problem.
#97Earlier quoted context omitted.
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?
Okay. To respond to both of you - I have put this in programming just to check, and I think you are taking a different inference from the question than I am. Under your inference, the man wouldnt have mentioned anything unless he had at least one male child. (in which case you can say the GG scenario is gone, but GB BG and BB are equally probable) Under my inference, the man just told me the sex of one child at rando…
"Under your inference, the man wouldnt have mentioned anything unless he had at least one male child. (in which case you can say the GG scenario is gone, but GB BG and BB are equally probable)"
No. I'm just assuming he has two children, and randomly mentions something about one of them. The GG scenario is only eliminated after he makes his statement, because we then know he has at least one boy.
Re: Think you understand Monty Hall? Try the Tuesday boy problem.
#98I've been thinking about this for an hour, and I'm now convinced that the author is wrong. The fact that we found out about one of the children from the father means that all probabilities are not equal, even though they're treated here like they are. The difference is between the information being offered, and determined independantly. I'll do this with the boy/girl problem, for simplicities sake. If we ask a man if…
0.48 ~ 0.5 Close enough for statistical purposes!
Re: Think you understand Monty Hall? Try the Tuesday boy problem.
#99ANYONE WHO SAYS THE ANSWER IS OTHER THAN 1/2: Let's simplify the question: If a man says "I have two children, one was born on a Tuesday," what is the probability that they are both born on a Tuesday? Is the answer to this 0 or 1/7 in your opinion? (Or something different).
You can follow a similar process to work out the probability as for the original question. For any two children, the possibilities are: Child 1 born Mon, Tue, Wed, Thu, Fri, Sat, Sun Child 2 born Mon, Tue, Wed, Thu, Fri, Sat, Sun We know that one of the children was born on a Tuesday, but we haven't said whether it's Child 1 or Child 2 (and that lack of information is key to understanding the original problem), so ou…
This is ridiculous. Let's do some queries on the world:
From all women: (some 3 billion)
the ones who have exactly two living children: x matches
the ones in which it is true for them to say "One of my children was born on Tuesday.". (this is true or false for every mother that comprises x. y mothers remain (can answer "true" for that question")
the ones that can say "both my children were born on Tuesday": z matches
are you telling me that sizeof z is 1/14th the sizeof y???
(because for me it is either 1/7 that size or exactly 0 if the correct meaning of "one of" is "exactly one of and not both of")
Re: Think you understand Monty Hall? Try the Tuesday boy problem.
#100Wait. What? The author says there can only be one BB but that there can be both GB and BG?
What he's doing here is saying that birth order functionally doesn't matter if the sibling is a boy, but it does matter if it's a girl. How is this correct?
If you keep comparing apples to apple you get:
Older Boy / Boy
Boy / Younger Boy
Older Girl / Boy
Boy / Younger Girl