Probability?

[Vexo]

So... I've got two kids...one is a boy, born on a Tuesday. What is the probability that I've got two boys?

Question posted in an engineering paper here, derived from a symposium. Curious to see what you guys think.

Come now, think about it yourselves, don't let Google think for you (at least not if you're gonna post it!).

[Sonna]

I did have an answer well 2 of them but was sure i was wrong as year 12 advanced math was so very long ago..

so chickened out and deleted my post

[Selinea]

Zero

Two kids and specified ONE is a boy

That's my guess anyway

[Eland]

Zero dps did you mean?

[Hiroki]

13/27

Can't argue with maths.. even when it's wrong

[Chunk]

50%

[Kofn]

Is that exactly the question as it was written on the test?

Because, linguistically speaking, if someone says "I have two kids... one is a boy, born on a Tuesday" there is a clear implication that the other kid is not a boy.

Probability doesn't enter into it, the speaker has effectively said that they have one boy and one girl (genetic mutations notwithstanding).

These puzzles tend to have a lot to do with language. If the speaker had said "the first is a boy".. blah blah blah... then the chance of the second being a boy is 50/50 (if we assume that the population at large has a 50/50 chance of birthing a boy or girl).

Since the actual phrase is "one is a boy", that could mean either the first one or the second one.

So the available combinations are:

B + B
B + G
G + B
G + G

It's obviously not G + G, leaving 3 other options. Again, assuming all combinations are equally likely (ie. people have 50/50 chance of birthing a boy or a girl). I would have to say the probability of two boys is 1/3 or 33%.

[Golgolath]

Was one of them born in Schrodinger's box?

[Jarinu]

Definitely liked cats I recon

[Tenam]

Well, if I remember correclty, if this follows the laws/rules of true randomness, and you figure that you (don't have any reproductive problems) are equally likely to have a boy as a girl, it doesn't matter how many kids you have or haven't had already. Each "flip of the coin" is 50% chance at "heads" or "tails."

[Tenam]

I've had some beers. Sorry, I think I mistook the question. What are the odds that you, out of the entire population are one of the dads who has two boys for two children, rather than one boy, one girl, or two girls? NFI.

[Naervhun]

hmmm I dont think its a 50/50 chance imo im looking at the fact that there are more women on the planet then men so yeah im going with the 30ish % chance.

[Vexo]

Since the actual phrase is "one is a boy", that could mean either the first one or the second one.

So the available combinations are:

B + B
B + G
G + B
G + G

It's obviously not G + G, leaving 3 other options. Again, assuming all combinations are equally likely (ie. people have 50/50 chance of birthing a boy or a girl). I would have to say the probability of two boys is 1/3 or 33%.

And is the probability then higher or lower when you factor in the fact that one is born on a Tuesday?

[Tenam]

Well, assuming that you could then follow the phrase with "And the other is a boy born on Friday" or whatever day, you could have two boys. If you're asking what are the chances of having another boy, the likelihood shouldn't change... should it? Curse you, Vexo, for confusing my brain!

[Vexo]

hmmm I dont think its a 50/50 chance imo im looking at the fact that there are more women on the planet then men so yeah im going with the 30ish % chance.

Statistics doesn't factor into it. I know I didn't disqualify it, but it's sorta implied (by the lack of information) that you approach it from a purely mathematical perspective.

That being said, there's appearantly a genetic preference in a lot of people for only birthing one sex, so the scale is actually tipped. That's irrelevant to the current question though.

And there are more women on the planet because they live longer.

[varutia]

Sounds like a trick question, 50% is the answer.

Statistically when preganacy happens, the ratio of boy to girl is 125 to 100, however boys tend to figure higher in abortion rate and die in a higher ratio after birth. I can not remember the exact age, but after a couple of years after birth the ratio of boy and girl should be roughly 50/50.

Strictly statistical wise, it is actually more likely to be a boy on birth.

[Kofn]

I can't figure out why Tuesday would be relevant in any way.

[Vexo]

I can't figure out why Tuesday would be relevant in any way.

You already had the right approach. BB, GG, BG and GB... expanding on that you've got B(Tue)B(Mon), B(Tue)B(Tue) etc. etc..

What's interesting to me, is that the more/better "clues" you get, the closer you get to the number everyone gives intuitively.

[varutia]

So... I've got two kids...one is a boy, born on a Tuesday. What is the probability that I've got two boys?

You question stated that the person had one boy already what is the chance of second one is a boy. This look like only two possibility

BB or BG

[Vexo]

So... I've got two kids...one is a boy, born on a Tuesday. What is the probability that I've got two boys?

You question stated that the person had one boy already what is the chance of second one is a boy. This look like only two possibility

BB or BG

The question asked was not "I have a son and my wife is pregnant, what will the sex of my unborn child be?".

GB is also relevant, since you don't know if the one stated is the oldest or youngest. So, four combinations total are possible, one is eliminated by what you know (one boy). One of the remaining three is the combination you're looking for and you're left with one chance outta three as being the probability.

[varutia]

So... I've got two kids...one is a boy, born on a Tuesday. What is the probability that I've got two boys?

You question stated that the person had one boy already what is the chance of second one is a boy. This look like only two possibility

BB or BG

The question asked was not "I have a son and my wife is pregnant, what will the sex of my unborn child be?".

GB is also relevant, since you don't know if the one stated is the oldest or youngest. So, four combinations total are possible, one is eliminated by what you know (one boy). One of the remaining three is the combination you're looking for and you're left with one chance outta three as being the probability.

Not true, only thing you can confer from the statement is that one of the two kid is a boy, then question ask what is the probability that I've got two boys. Statistic wise, it is still a 50 percent chance that other kid is a boy, as each case is independent of each other and have no direct relevancy.

[Kofn]

Your assertion is only true if you assume a birth order Var

Probability calculations are a mindfuck and humans are inherently bad at doing them "intuitively".

This birth thing is a similar type of problem to the "should you switch doors" problem shown in the movie 21.

[Creac]

Vexo - you didn't answer Weo's question about the grammar of the question you posed? Is that exactly accurate? If it is, it's badly flawed.

[varutia]

Your assertion is only true if you assume a birth order Var

Probability calculations are a mindfuck and humans are inherently bad at doing them "intuitively".

This birth thing is a similar type of problem to the "should you switch doors" problem shown in the movie 21.

No, birth order do not matter with the information provide in Vexo's question. Only information Vexo gave are "2 kids" and "one is boy". The event of other kid being boy or girl is completely independent of the known boy, so the chance of the other kid is a boy is equal to it being a girl. Whether the other kid is born earlier or later than the known boy does not have any affect on the probability it being a girl or boy as it is an independent event by itself.

[Selinea]

This thread is making my brain hurt