You are tossing coins/determining sex positionally with that code. It is invalid for my argument.

No I'm not. I'm comletely ignoring position. In both lines, the positions are treated completely equally. We have

if (r1 == 1 or r2 == 1)

and

if (r1 == 1 and r2 == 1)

in another. Where am I treating coins "positionally"?

Oh and to whoever it was got upset about the "my applied math" I was very clear that it was an actual book on Applied Mathematics. Had I said "The Handbook of Chemistry and Physics" would you have had a fit? It, unfortunately, won't be in there although I do have one from 1984 (high school graduation present).

Put another way: the first line just means if EITHER number is odd. The second line just means if BOTH numbers are odd. Neither position is distinguished.

By virtue of the existence of R1 and R2 being tossed separately, they are positional. R1 was tossed first and R2 tossed second.

OK. Then do it as in my initial code:

r = random number.

If (first bit of r = 1 or second bit of r = 1)

If (first bit of r = 1 and second bit of r = 1)

Then they're both tossed at the same time. Better?

The proper way would to be a single random number indicating the total dots with each side having zero or one dot. (consider them chromosones). You then have three possible outcomes when the coins are stacked together and tossed at the same time, 0, 1, and 2 dots. Only 1 dot and 2 dot results would be tallied and split and matching respectively.

The bits are positional

My original claim was this: if you are told that a fair coin was tossed twice, and that one of the tosses was heads, then the probability that the other toss was heads is 1/3. Do you agree or disagree?

"The proper way would to be a single random number indicating the total dots with each side having zero or one dot. (consider them chromosones). You then have three possible outcomes when the coins are stacked together and tossed at the same time, 0, 1, and 2 dots. Only 1 dot and 2 dot results would be tallied and split and matching respectively. "

That algorithm is notable for not, in fact, simulating two coin tosses (or two births). There is only one random event, so certainly there is no independence.

Please answer the question in my prior post when you respond.

@draug, I can't believe after the shit you gave synapse, you're arguing this the way you are. There are 4 equally possible outcomes (the reason for mentioning even prob) of tossing 2 coins or tossing 2babies) I've seen you list these out for synapse! In this example, one assumption just eliminates one of the possible outcomes (a point I missed at first thought and you corrected). That leaves 3 possible outcomes. Only one of those possible outcomes is favorable, therefore prob = fav/pos = 1/3.


You'd better hurry up and admit you're wrong, before synapse sees this and has a field day with you!

You are now actually arguing HIS POINT, that there is a difference between consecutive throws and simultaneous throws ...

You stalked him for days trying to get him to admit he was wrong ... Did he end up convincing you?

Ah! The coin toss would have twice as many chances of a split versus 2 of a specific side (because two of the other side is eliminated). I was arguing the odds of the second being boy or girl don't change just because another one was a boy or girl. So yes, the coin toss is 1/3 double heads versus 2/3 a head and a tail. But that is positional and not about the odds of a single throw which is not affected by any other throw.

So it comes down to the odds of any given child or coin are 50/50 regardless of the others outcome. So maybe my flaw is that I am thinking positionally (boy was first) and not thinking in combinations.

Does this mean you are about to go platinum, Draug?

Draug, it's the same thing. Each birth is a 50/50 chance, i.e., a coin toss.

The children, too, are positional, just like the coin toss (one is older, for example), although, just like the coin toss, we are not told which one is a boy, but only whether one IS a boy.

You are just making up fake concepts now. Please present rigorous arguments.

OK, Draug, I wrote that before I saw your last post. Sorry.

Yep, I think that's it.

FWIW, I don't consider Draug owes any money, since he seems to have changed his mind without agreeing to code and running it.

It'll have to wait until June (have an expensive wedding to attend out of town in May), but I will give the $100.

Split the dif, semck. If you can afford 50 so can I and we give it in alderian's name?

Maths/probability is not my strong point. And I am finding it hard to get my head around this problem.

I just made a test case of this question using Excel and a sample of 10,000 of father with two children, where the sex of the children were both random.

These were the results:
Boy, Boy 25%
Boy, Girl 25%
Girl, Boy 24%
Girl, Girl 26%

But if I filter the results on where the first child was a boy:
Boy, Boy 50%
Boy, Girl 50%

What is wrong with the above and why does it differ from the correct answer 1/3?

This quote seems appropriate.

"There are lies, damn lies, and statistics"
This paradox falls firmly in the last category. Which is to say, an artifact of absurdity.

And my flaw was I perceived that knowing one was a boy meant I met that one, so there was another one who has a 50 50 shot at being a boy. But if viewed as not knowing either child it does become combination probabilities not a single toss probability.

I appreciate it, Draug -- that's generous, but I can't really afford 50 right now. ; ( I only made the bet because I knew my position was right. (If I'd lost, I'd have paid, but it would have hurt a lot).

You can pay or not as you prefer. As I say, I was pretty explicit it was a bet once you accepted code and we ran it blind, which did not happen. So I won't hold your feet to the fire if you choose not to donate, but it's up to you.

That was the point of mujus's clarification, and semck's rephrasing, to avoid that specific confusion that his original question had in it. See replies 3 and 6.

@spy - you have the same flaw I did. *We* were thinking positionally. We don't know that the first wasn't a girl and the second a boy.

"But if I filter the results on where the first child was a boy:
Boy, Boy 50%
Boy, Girl 50%"

The missing category is Girl, Boy. Which is equally probable.

Wow a lot of posts in between, that was regarding draug assumption that the first was a boy. The original question had that in it, and it was clarified.

And there was never an acceptance of the bet. draug proved his honor with that last donation, don't try to guilt him into this one,

Thank god you came around though, I was worked for a minute.

Worked = worried

"And there was never an acceptance of the bet. draug proved his honor with that last donation, don't try to guilt him into this one[.]"

I agree. That is what I was intending to say, so let me say it again if I didn't do so explicitly. Draus is welcome to donate any money he wants any time, but it won't be because of this bet, because it was never formed.