A man has two children. One of them is a boy.

[Triggaaar]

It's your fixation with the '2nd child' that is preventing you from seeing the alternative logic, I think.

I don't think I've missed the alternative logic, I explained the alternative logic in post #97 and you replied saying "this is pretty much exactly the logic behind my argument."

Its (at least) one of them - not that one IS a boy and what is the other.

I know what you're saying with regards to the original question, and how it can be interpreted differently. What I'm specifically disagreeing with is your answer to my simple question in post #113 and your answer in #116. Your answer (1 in 3) was wrong (despite the late edit).

Anyway, far more emminent mathematicians than you or I had decreed that both answers are valid. I'm happy to go with that.

As you say, the problem with the original question is about ambiguity, not probability, so maybe a professor in English or linguistics would be more appropriate than a mathematician. But it's not the original question we're arguing over, it's the simplified example I gave, which you still disagreed with. Your battle isn't really with me, it's with your pride

 

[hans kraay fan club]

I don't think I've missed the alternative logic, I explained the alternative logic in post #97 and you replied saying "this is pretty much exactly the logic behind my argument."

I know what you're saying with regards to the original question, and how it can be interpreted differently. What I'm specifically disagreeing with is your answer to my simple question in post #113 and your answer in #116. Your answer (1 in 3) was wrong (despite the late edit).

As you say, the problem with the original question is about ambiguity, not probability, so maybe a professor in English or linguistics would be more appropriate than a mathematician. But it's not the original question we're arguing over, it's the simplified example I gave, which you still disagreed with. You're battle isn't really with me, it's with your pride

I'm not going to drag this out arguing about exactly what we're arguing about. And I'm certainly not continuing this in MY own (as opposed to work) time...

I bid thee farewell, pride intact.

 

[Megazone]

When you're an old man rocking in your chair. You'll look back and remember debates like these being the making of you.

Keep rocking in the real world.

 

[Leyton Gull]

I don't think I've missed the alternative logic, I explained the alternative logic in post #97 and you replied saying "this is pretty much exactly the logic behind my argument."

I know what you're saying with regards to the original question, and how it can be interpreted differently. What I'm specifically disagreeing with is your answer to my simple question in post #113 and your answer in #116. Your answer (1 in 3) was wrong (despite the late edit).

As you say, the problem with the original question is about ambiguity, not probability, so maybe a professor in English or linguistics would be more appropriate than a mathematician. But it's not the original question we're arguing over, it's the simplified example I gave, which you still disagreed with. Your battle isn't really with me, it's with your pride

'You know Pete's got a couple of kids' 'Oh yeah? Girls or boys' 'well one of them is a boy, Pete introduced me to him' 'oh well in that case the chances are the other one must be a girl' 'how do you work that out?'

 

[KJP]

This reminds me of this in scrubs

http://youtu.be/ezF_JO8agR0

 

[Seagull58]

Yes.

That was just a way of making a number to help people think about the problem.

For HKFC:

We could make it 4 couples if you like. One has 2 boys, one has 2 girls, two couples have one of each.

You ask a random couple to tell you the gender of one of their children. The couple says they have a boy.

There is a 50% chance their second child is also a boy.

If you ran the same test 4 times, on average 2 times the couple you chose would have said 'boy' and 2 times the couple you chose would say 'girl'.
Of the 2 times that the couple said 'boy', 1 time they would also have a girl, 1 time they would have 2 boys.

No, there's a 33.3% chance the second child is a boy. Of the 4 couples you have eliminated the GG couple and you're left with 3 couples. Only 1 of those 3 couples has a second boy.

 

[Seagull58]

Two coins:
One coin has already been flipped and has landed on heads (boy).
The probability that the second coin will land on heads is 1 in 2.

The answer to the ridiculous question is; there's a 1 in 2 chance the other child is a boy (or the second coin to be flipped lands on heads).

No, because he didn't say the first child was a boy, as in it is not the case that the first coin is a head. Only one of the coins must be a head so you must include the probability of the first coin being a tail.

 

[Seagull58]

But why were we told one was a boy, why weren't we told one was a girl? This is part of the facts, and you're overlooking it. But even if we can't take it from the original question, we can take it from subsequent questions we've posed, and you've still tried to argue that it's 1 in 3, and it's not.

You've been happy to go with my example of 4 families - you can do the same with the 100 families, or the whole population, and the answer is the same - 50%.

In our example of 4 families, on two occasions the couple come forward and say 'boy' and on two occasions the couple come forward and say 'girl'. It doesn't get simpler than that, I don't know what more you want.

Your logic is incorrect. I'm with HKFC on this. The fact is that at least 1 child is a boy. therefore only 1 of the 4 couples is eliminated and the probability of the second child also being a boy is 1 in 3. The question is nothing to do with asking couples what sex one of their children is. That would be a different question.

 

[nwgull]

No, there's a 33.3% chance the second child is a boy. Of the 4 couples you have eliminated the GG couple and you're left with 3 couples. Only 1 of those 3 couples has a second boy.

You've also eliminated GB by saying that the first child is a boy, as is effectively the case here. Therefore, it's 50/50 and anyone arguing otherwise is wrong.

 

[Seagull58]

You've also eliminated GB by saying that the first child is a boy, as is effectively the case here. Therefore, it's 50/50 and anyone arguing otherwise is wrong.

NO. It doesn't say the first child is a boy. It says one child is a boy. Both children have already been born.

 

[TonyW]

Ok there's 15 pages of this, so it may have been said, but the full stops could be used to separate the original post into 2 unrelated statements and an unrelated question.
Thereby making the whole thing impossible to answer.
Again, apologies if someone has already spotted that fact.

 

[nwgull]

NO. It doesn't say the first child is a boy. It says one child is a boy. Both children have already been born.

Either the boy is the first child, in which case it eliminates GB, or the boy is the second child, in which case it eliminates BG. Either way it leaves you with 2 out of 4 options: 50/50.

 

[Triggaaar]

No, there's a 33.3% chance the second child is a boy. Of the 4 couples you have eliminated the GG couple and you're left with 3 couples. Only 1 of those 3 couples has a second boy.

Your logic is incorrect.

Don't know if you're trolling, haven't read the whole thread or what, but the logic is right.

nothing to do with asking couples what sex one of their children is.

It's a separate question to the OP. The question I've posed involves asking couples what gender one of their children is, so for you to now say that it's nothing to do with asking couples is ridiculous, since that's the question I've posed.

 

[AlbionPics&SouthCoastTwit]

This reminds me of this in scrubs

http://youtu.be/ezF_JO8agR0

This truly exposes the problem with healthcare in America. All Americans are too dumb to figure out that they charge too much.

 

[mreprice]

Don't know if you're trolling, haven't read the whole thread or what, but the logic is right.

It's a separate question to the OP. The question I've posed involves asking couples what gender one of their children is, so for you to now say that it's nothing to do with asking couples is ridiculous, since that's the question I've posed.

Unfortunately you have made up the bit about asking the couple to name the gender of one of their children. That isn't in the question.

Take your four couple example that is spot on. You are talking to one of the couples selected at random. A boy walks up and they say hello son. What is the probability that couple has two boys?

It's one in three.

 

[mreprice]

Actually I have made the same mistake you did. At least I see know why some people are so confused.

If you ask "what is the gender of one of you children?" The answer is 50%. If you ask "do you have at least one boy?" then the answer is one in three.

The actual question is nicely ambiguous!! I'll accept it could be interpreted either way.

 

[Moshe Gariani]

Actually I have made the same mistake you did. At least I see know why some people are so confused.

If you ask "what is the gender of one of you children?" The answer is 50%. If you ask "do you have at least one boy?" then the answer is one in three.

Is it beer o'clock in Sydney?

What on earth are you on about?!

 

[Triggaaar]

Unfortunately you have made up the bit about asking the couple to name the gender of one of their children. That isn't in the question.

I didn't just make up that bit, I made up the whole question that Seagull58 is referring to. It wasn't the original question, I was asking another question that didn't have the ambiguity of the original, so that we could clear up the disagreements over probability and ambiguity.

Take your four couple example that is spot on.

What is spot on? I said that if a random couple walked up and randomly told you the gender of one of their children, and they said 'boy', it's a 50% chance that the other is too. Seagull58 (and HKFC gace him the thumbs up even though he's already realised he was wrong) says it's 33%. He's wrong.

You are talking to one of the couples selected at random. A boy walks up and they say hello son. What is the probability that couple has two boys?

It's one in three.

To be clear about your question - you were talking to one couple, at random, and one of their two children randomly walked up, and it happened to be a boy (could have been a girl). The chance of his sibling being a boy is 1 in 2.

 

[Triggaaar]

If you ask "what is the gender of one of you children?" The answer is 50%. If you ask "do you have at least one boy?" then the answer is one in three.

Yep.

 

[Triggaaar]

The actual question is nicely ambiguous!! I'll accept it could be interpreted either way.

To be honest, the first question is still 1 in 2. The only way it could be 1 in 3 is if the person posing the question deliberately looked for a man with a boy, and even then it depends on how the man was selected. And that's not a reasonable assumption from the question.

The only fair assumption it's possible to make is that the man was chosen randomly and that we were randomly chosen the gender of one of his children. And it's 1 in 2.