No, there aren't two random coin tosses, only one, because the second coin *must be* heads (or the first coin must be heads).

No, Draug. All we know is THAT there is AT LEAST ONE BOY. That is *completely equivalent* to saying that *It is not two girls* (with no why or anything else).

You are just making crap up. Write a simulation that actually includes two random flips or we're done here.

how is it not obvious that either the one on the left has to be heads or the one on the right does, and that 50% the one on the left is heads the one on the right will be heads (if we go down the left route), and that 50% the one on the right is heads so will be the one on the left (if we go down the right route)? your problem, as i've said, is giving to much importance to order (which is irrelevant in the OP), for an independent conditional probability question. we know one is heads so we can say H, now we need to see the other one as T/H. this is just like the case i said where we showed you a head.

how about this semck, this is my simulation for you to run, throw two coins without looking. we agree each coin has a fifty fifty chance of being heads yes? now i remove a coin - either the left or the right, you don't know. what are the chances of the remaining coin being heads? 50-50 right? this is the same, i've removed a child at random (older or younger) because i know it's a boy, but this doesn't miraculously change the probability of the remaining child....

The situation I described, *again*, was:

"[Y]ou know only that (a) two coins were tossed and (b) at least one was heads"

Notice the part where I said that two coins were tossed? We're talking about the outcome of *two random events.* You know AFTERWARD that the outcome of two RANDOM events gave at least one head. The situation you're describing is this:

"You know only that one coin was placed on a table with a heads up, and another coin was tossed."

Then we are done because my simulation takes into account that the first coin is heads by forcing it heads and randomly tossing coin two then accoutns for the second coin being heads and only tosses the first coin. Your allows a factor that is impossible and then ignores it, thereby altering the observation. That factor being two tails. The rules do not allow for two tails to eve come up so ever allowing to tails to happens negates the simulation.

But we also know that one random event was heads. Period. So allowing for and then discounting an impossible outcome (double tails) negates the experiment. Let's review basic experimental science: remove variables that may or may not have an effect on the outcome. TT may or may not have an effect on the outcome so we design the experiment to never let them happen.

Draug, I will try to explain it one more time in the "known unknown" language you are trying to use. Let's consider all of the possibilities for his two children:

GG - Obviously this case is out.
BG - In this case our "known"child is the first one and the unknown is a girl
GB- In this case our "known" child is the second one and the unknown is a girl
BB- In this case there is not a predetermined "known" child. We can arbitrarily choose the first kid to be known if you want, and then the "unknown" child is a boy.

It seems like your argument is that for some reason the third case has to be given double weight. There is no justification for that, but I want to hear what you think it is. Please do not re-frame what I am saying to say that you choose "known/unknown" before the BB/BG/GB/GG combination. Please either explain why you think it is logically unsound to pick the BB/BG/GB/GG combination first, or why (without reframing) there is any justification for doubling the weight of the third case.

In fact, Monty Hall demonstrates this perfectly. Each door has a one in three chance of having the car and a two in three chance of having a donkey. Each coin has a 50 50 chance of being heads and a 50 50 chance of being tails. Eliminate the impossible from the experiment (TT) by never allowing it to happen. If you allow TT to happen then you have corrupted the experiment because you have found a condition that doesn't meet the requirements of the experiment.

Draug,

The outcome GG was not impossible beforehand. It is only impossible after the two flips. Do you actually think it is impossible to have two girls?

No. It is impossible only after we know, *after* the fact, that there is at least one boy. But you have to allow the outcome, because that is the nature of independent coin tosses.

uclabb, Draug is now saying we have to exclude GG from the outset as even a possibility and just set the older boy to B because we know GG didn't happen.

If KG is included, the KB must be included. If GK is included then BK must be included. It is a matter of discrete versus non-discrete probabilities.

Draug, please see my other thread, "A request for a generous mod."

And no, I said you must run it once with the first child as B and again with the second child as B (age , alphabet, random number pulled out of the hat, makes no difference as they are discrete objects with a state).

@SD- You said this
"how about this semck, this is my simulation for you to run, throw two coins without looking. we agree each coin has a fifty fifty chance of being heads yes? now i remove a coin - either the left or the right, you don't know. what are the chances of the remaining coin being heads? 50-50 right? this is the same, i've removed a child at random (older or younger) because i know it's a boy, but this doesn't miraculously change the probability of the remaining child...."

This is not the same. The analogy is not removing a coin. The analogy is specifically removing a coin that landed heads (and, in particular, that there was a coin that landed heads up to remove). This seems to be the distinction that you are missing.

Draug, you didn't answer my question. I hope that you do.

Draug is right and saying what I was failing to find the word to say earlier, about the impossibility of gg meaning we have to look at it differently. Here we can remove the boy and we know there is a child that is a boy!

If you remove gg as a possibility a priori, you are certainly not talking about the results of any process whereby a 50/50 choice was taken twice, SC. Independence is out the window.

I swear to God this site drops replies on occasion because I did give an absolute answer. I said that yes, the odds were 50/50.

The ruels removed it as a possibility, we did not. We designed the experiment to fit within the rules of the question. You did not.

Draug's version and its premises: we have at least one boy with our two children. we can label child one A and child two B. The child that we know the sex of has equal chance of being A and equal chance of being B. 50% of the time the KNOWN child is A and 50% of the time the KNOWN child is B. 50% of the time the KNOWN child is A the UNKNOWN child is also a boy and 50% of the time the KNOWN child is A the UNKNOWN child is a girl. 50% of the time the KNOWN child is B the UNKNOWN child in A is a boy and 50% of the time the UNKNOWN child in A is a girl. So either way it is 50/50 for the other child. Or alternatively, we could say that 50% of the time the KNOWN child and the UNKNOWN child have the same sex (as shown above), so 50% of the time there are two boys in this situation.

Draug, the rules don't remove it as a possibility. That would be to say that it is NOT two tosses of a fair coin. The rules remove it as a RESULT. They talk about the totality of results from two tosses of a fair coin in which information after the process has eliminated the TT as a possible result.

You are implicitly changing to another process than two fair flips.

We have two children. In this universe we know at least one is a boy. In this universe two girls is impossible. Therefore they must be removed form the experiment.

Draug, can you please respond to my question? Here it is reproduced for easy reference:

"I will try to explain it one more time in the "known unknown" language you are trying to use. Let's consider all of the possibilities for his two children:

GG - Obviously this case is out.
BG - In this case our "known"child is the first one and the unknown is a girl
GB- In this case our "known" child is the second one and the unknown is a girl
BB- In this case there is not a predetermined "known" child. We can arbitrarily choose the first kid to be known if you want, and then the "unknown" child is a boy.

It seems like your argument is that for some reason the third case has to be given double weight. There is no justification for that, but I want to hear what you think it is. Please do not re-frame what I am saying to say that you choose "known/unknown" before the BB/BG/GB/GG combination. Please either explain why you think it is logically unsound to pick the BB/BG/GB/GG combination first, or why (without reframing) there is any justification for doubling the weight of the third case."

If I know that oxygen causes a bacteria to grow but I want to see the effect amonia has on it versus chlorine, then I have to conduct my experiment in an oxygen free environment. If I want to see what effect knowing one of the kids is a Boy has on the outcome, then I have to remove any possibility of GG coming up. Dude, it is simple Scientific Method.

But you also know that they were the result of a fair 50/50 process applied twice. Just because we know partially the results does not change the nature of the process that led to them (which is crucial in computing probabilities).

Here is what you have agreed to as a characterization of your position.

"If you know only that (a) two coins were tossed and (b) at least one was heads, there is a 50% chance that both coins were heads."

"I swear to God this site drops replies on occasion because I did give an absolute answer. I said that yes, the odds were 50/50. "

I answered it. Christ you are dense!

We know two aspect to these partial results, one thorough observation and the other through deductive reasoning. Eliminate the impossible from the experiment.

"I answered it. Christ you are dense! "

I would like to believe that some day, you will view this post with irony. Sadly, that hope is waning.

That's not an answer. You didn't respond to anything I said.