Puzzle: I have two children ...

[littlebabyjesus]

shit, I've got to do some work now.

But have a think, kabbess. I'm right about this.

 

[littlebabyjesus]

But I don't know whether the fact that one would be a boy is something that was inevitable or something that was random.

Doesn't matter.

Either way, the probability that one is a boy now that you've been told that one is is 1.

 

[kabbes]

The kabbess is my wife and she'll tell me to STFU if I tell her to think about it.

Anyway, you've got work and I'm going home in 10 mins. So this will have to rest.

And YOU think about it, you crazy fool! Or, at least, you're going to have to come up with a good reason why counting the different options as per earlier in the thread ALWAYS leads to the wrong answer, if that's the tree you're barking up...

 

[beesonthewhatnow]

Nope. I mean that there is no first one until some information about them has been given. Once you have information about one but not the other, they are then given an order if you are only considering the information given.

The answer to the OP is also 50/50 by extension of the same principle.

You are wrong.

 

[littlebabyjesus]

You are wrong.

I am very right, and have attempted to explain why. I'll try again when I have more time, because my explanations are obviously not working so far.

This is a case of mathematicians tying themselves into logical knots to reach an idiotic answer. The logic is faulty, and the answer is wrong.

 

[MightyAphrodite]

i dont get it.


although this pic and quote from the link made laugh , and also made me a little glad i dont 'get it'

Getting together for some mathematical fun



fun? for real? different strokes.

 

[beesonthewhatnow]

This is a case of mathematicians tying themselves into logical knots to reach an idiotic answer. The logic is faulty, and the answer is wrong.

No, it's a result of probability not often giving "logical" answers.

Have a read of The Monty Hall Problem for a similar example.

 

[littlebabyjesus]

No, it's a result of probability not often giving "logical" answers.

Have a read of The Monty Hall Problem for a similar example.

Nope. That is different. It has to do with what you know when.

 

[beesonthewhatnow]

Nope. That is different. It has to do with what you know when.

It's similar in that a seemingly "obvious" answer isn't the correct one.

As the original puzzle is stated the answer is 13/27. Not obvious, not "logical", but correct nonetheless.

 

[littlebabyjesus]

It's similar in that a seemingly "obvious" answer isn't the correct one.

As the original puzzle is stated the answer is 13/27. Not obvious, not "logical", but correct nonetheless.

No. Sorry, I'm fully aware of the Monty Hall problem, whose solution only becomes clear once you have examined what you know and when you know it.

Do the same with this problem and the answer is 50/50

There is nothing illogical about the Monty Hall problem's solution. It only appears counterintuitive at first to many because their intuition is set up wrongly.

 

[Santino]

Consider:

You approach a man you know to have two children, of unknown sex.

What are the chances that they are of different sexes?

edited to add: Scratch that, it gets us nowhere.

 

[beesonthewhatnow]

Do the same with this problem and the answer is 13/27

Which is what I said. You were saying the answer is 1/2 or 50:50

 

[littlebabyjesus]

Which is what I said. You were saying the answer is 1/2 or 50:50

Sorry, yes, I just edited. Do the same with this, and you get 50/50 for the reasons I've given.

I'll try to explain fully later.

 

[beesonthewhatnow]

Sorry, yes, I just edited. Do the same with this, and you get 50/50 for the reasons I've given.

But you don't. Look at my first post on this thread.

 

[littlebabyjesus]

But you don't. Look at my first post on this thread.

Have you read my posts? I've dealt with this. At the point of consideration, you know that:

there are two children

one is declared

the other is undeclared

The children are thus fixed in one order so long as you are considering the qualities that have been declared.

Thus, the chances of girl/boy are not 13/27, but 7/14: ie chances are 50/50

 

[Crispy]

It's similar in that a seemingly "obvious" answer isn't the correct one.

As the original puzzle is stated the answer is 13/27. Not obvious, not "logical", but correct nonetheless.

No, only if the original question is amended to

I have two children, only one is a boy born on a Tuesday. What is the probability I have two boys?

 

[littlebabyjesus]

No, only if the original question is amended to

I have two children, only one is a boy born on a Tuesday. What is the probability I have two boys?

Correct. Because you are now giving information about the second child: it is not a boy born on a Tuesday.

Probability is all about what you know and when you know it. As the problem is stated, you know nothing about the second child.

 

[beesonthewhatnow]

No, only if the original question is amended to

I have two children, only one is a boy born on a Tuesday. What is the probability I have two boys?

No, because the 13/27 answer allows for 2 boys both born on a Tuesday. It's one of the 27 possible combinations of children.

 

[Crispy]

No, because the 13/27 answer allows for 2 boys both born on a Tuesday. It's one of the 27 possible combinations of children.

EDIT.... arrgh type it right crispy you fool

 

[ATOMIC SUPLEX]

This reminds me of when I made a seemingly five gear system that had over 100% efficiency. One cog was irrelevant but at first glance seemed to be part of the system.

 

[littlebabyjesus]

No, because the 13/27 answer allows for 2 boys both born on a Tuesday. It's one of the 27 possible combinations of children.

Please read my posts. I have dealt with this.

One child is now fixed. You are only now dealing with one child. There are 14 possible combinations, seven of which are boy, seven girl.

 

[beesonthewhatnow]

Please read my posts. I have dealt with this.

You haven't.

 

[littlebabyjesus]

You haven't.

You may not have understood it, but I have.

Anyway, I have to work.

 

[ymu]

shit, I've got to do some work now.

But have a think, kabbess. I'm right about this.

No, you're wrong. You're deciding to assign the declared child in the first position but then forgetting to double the probability of BG (because it's now identical to GB when you don't arbitrarily assign it the first position).

All you have to do is write down all the possible combinations in a family to work out the denominator and then knock out all the ones excluded by the information to work out the numerator. You're trying to take a short-cut on the number of combinations you have to write down but forgetting to adjust the probabilities accordingly.

 

[littlebabyjesus]

No, you're wrong. You're deciding to assign the declared child in the first position but then forgetting to double the probability of BG (because it's now identical to GB when you don't arbitrarily assign it the first position).

All you have to do is write down all the possible combinations in a family to work out the denominator and then knock out all the ones excluded by the information to work out the numerator. You're trying to take a short-cut on the number of combinations you have to write down but forgetting to adjust the probabilities accordingly.

Nope. I haven't forgotten that, but I'm obviously failing to explain myself. I'm surprised how many able mathematicians are getting this wrong, tbh.

 

[Crispy]

In the OP, can the state of Child 1 affect the state of Child 2? What information, in the OP as stated, prevents the 2nd child from being a tuesday boy? If nothing prevents Child 2 from being a tuesday boy, then all possible children are possible. Half of all possible children are boys. The probability is 1/2. Add the "only" to the question in the OP, and you get the other answer.

two tuesday boys are allowed in the OP's question

 

[beesonthewhatnow]

You may not have understood it, but I have.

No, you are making a fundamental error by assuming that by declaring that a boy is born on a Tuesday that you are also declaring his position in the birth order.

"One boy is born on a Tuesday". That's it. You have no more information. They could be the first or second child.

You then get the number of combinations I listed in my first post.

 

[ymu]

Nope. I haven't forgotten that, but I'm obviously failing to explain myself. I'm surprised how many able mathematicians are getting this wrong, tbh.

Thing is, the correct answer is very well known, and it's not the one you're giving us. You might want to stop and wonder why that is rather than just repeating that you're right.

 

[beesonthewhatnow]

I'm surprised how many able mathematicians are getting this wrong, tbh.

Likewise

 

[littlebabyjesus]

In the OP, can the state of Child 1 affect the state of Child 2? What information, in the OP as stated, prevents the 2nd child from being a tuesday boy? If nothing prevents Child 2 from being a tuesday boy, then all possible children are possible. Half of all possible children are boys. The probability is 1/2. Add the "only" to the question in the OP, and you get the other answer.

in the OP, tuesday boys are not knocked out of the matrix

Yes. And to answer the objection that everyone seems to be getting wrong, the order of Child1/child2 is fixed by the declaration of one of the children. That is the order: declared; undeclared, as your knowledge stands at the point of working out the probability.