A riddle my brother gave me today (page 4)

MissingLink

Did you mean that the other one can't be a boy born on a tuesday also? If that's the case, then I'll go for 6/14 (42.86%)

MissingLink: No. to paraphrase: "A person has two children. One of them (in the strict sence: At least one) is a boy born on a tuesday. What is the probability the other is a boy?". Is it clear? I can see that "one" is a bit ambigious, but i thought it was the best word to use in english.

Another way to understand the question is this:

"A man has two children. You ask him if any of his childrens is a boy who was born on a tuesday. The man says yes. What is the probability both his children are boys?"

John Doe

JD - changeling is only wrong if one assume that no couples has more likelihood to have boys than girls. I am not a biologist, but i believe that is wrong.

You stated the assumption was that the probability of having a boy is 1/2.

we assume a-priori there is a 1/2 chance to give birth to a boy independent of past births, no twins, and no more boys or babies are born on tuesdays than other days of the week

A probability is nothing more than the ratio of a possible occurence to a possible non occurence. This is determined solely by the enumeration of possible outcomes. A particular occurance in a specific chance has no bearing on the probability of the next occurance. Therefore, the statement that the more boys you have the higher the chance the next one will be a boy is patently and conclusively false.

changeling

LOL! I knew that... :)

bohm

John Doe: Well, since i just watched the world cup and had a couple of beers i dont care to go off-topic or might sound rude. Pardon me, and take this as a constructive argument from one professional to the other!

You wrote:

"A probability is nothing more than the ratio of an occurence to non occurence. This is determined solely by the enumeration of possible outcomes. A particular occurance in a specific chance has no bearing on the probability of the next occurance. Therefore, the statement that the more boys you have the higher the chance the next one will be a boy is patently and conclusively false."

Now lets review my actual statement:

Side note for changeling: You are right, ff one assume a given couple generate boys with a probability a, the more boys they have (compared to girls) the higher our estimate of a will be, and we will estimate the probability their next children is a boy to be higher. a does not increase exponentially, though.

In the problem, we neglect this effect and assume a=1/2 for both births. Ie. i ask the problem under the most simple assumptions.

So its pretty damn clear i never wrote the probability the next will be a boy will be higher, i wrote our belief the next will be a boy will increase. That you begin your post by writing that: "You stated the assumption was that the probability of having a boy is 1/2. " is a red herring, since i clearly indicated that i was NOT discussing the riddle with my post by my last statement which i have underlined.

Thats a statement i stand to. You still think i am wrong, or did you misread my post to changeling?

For everyone else: I want to emphatize that in the riddle i assume the mom had a 1/2 chance of giving birth to a boy at both births. Its not a trick question, and there is no "smartass" solution (i hate riddles like that!).

bohm

JD - any update?

Mad Sweeney

Bohm, you have already said that we are ignoring the fact that a father is likely to produce more of one sex than the other and that the probability is half and half, correct?

If that is so, then John Doe is correct. This problem, therefore, is no different than a coin toss. The probability is ALWAYS going to be 50-50 or 1/2 and 1/2. Previous trials have NO EFFECT on subsequent trials, once you have precluded the biology from the issue, which you have.

In reality, however, the chance of the second child being a boy is EXACTLY THE SAME as the chance of the first child being a boy. The only way to know what that rate is, is to take a series of sperm samples and run genetic tests on them. But again, since the scenario gave that data as 1/2, then it remains 1/2 for ALL offspring of that father.

bohm

Mad S.:

Its very important not to confuse the riddle with with my reply to changelings post and subsequent discussion with JD. Im sorry if this is confusing. I wrote:

JD - changeling is only wrong if one assume that no couples has more likelihood to have boys than girls. I am not a biologist, but i believe that is wrong.
Nevertheless - this is completely offtopic.For the riddle, just assume the women is question give birth to boys with probability 1/2 irregardless of her history.

i believe i make it clear here, especially in the last line, that i see these two things as two seperate issues. So speaking in the context of the riddle i will repeat what i wrote before: "I want to emphatize that in the riddle i assume the mom had a 1/2 chance of giving birth to a boy at both births.".
Also look at the clarification i wrote to ML.

The key is that the sexes of the two boys is not independent of each other given the information, for example we exclude the possiblity both are girls. I can say this much: the right result (at least my result!) is not 1/2.

-----

Returning to the discussion regarding Changelings post and my exchange with JD

You wrote: In reality, however, the chance of the second child being a boy is EXACTLY THE SAME as the chance of the first child being a boy. The only way to know what that rate is, is to take a series of sperm samples and run genetic tests on them. But again, since the scenario gave that data as 1/2, then it remains 1/2 for ALL offspring of that father.

You are completely right that if we assume the couple produce boys with probability 1/2, and births are independent events, then even if they had 9 boys the chance the next child was a boy would still be 1/2. But that was not what i wrote. As i showed in my previous post JD misquoted me (i dont assume malice, i think he made a honest mistake) and i still stand by what i originally wrote.

One think i did get wrong, in my beer-induced post world-cup state was that i wrote likelihood instead of probability. JD should have landed on top of me like a ton of bricks for that one!

TheSilence

If you flip a coin 19 times and get heads there is still a 50/50 chance that if you flip it again you will get heads. Whether or not a pregnant parent will have a boy or a girl is not in any way effected by the gender of previous children. It is still a 50/50 shot. If you are asking about the probability of 1 child it will always be 50/50.

Now, if you are going to ask about *2* unknowns then you can factor it in. 2 sisters are pregnant, what is the probability they will both have boys? Then the fact that you are comparing 2 unknowns will effect the probability and you will end up with a 1 in 4 shot that they will both be boys. But in the scenario you provided there is only 1 unknown and, therefore, the only probability is based on that one unknown which is a 50/50 shot. You are falling into a trap that many fall into. Random acts such as this are not biased by previous random acts, otherwise they would not be random.

Jackie

bohm

TheSilence: You are completely correct, without any other information the chance both children are boys is 1/4, because the two events are independent. But you fall into a trap that you dont take into account that additional information can make two independent events non-independent. That change the picture, IMHO. I will give my result tomorrow :-).

once again: "A man has two children. You ask him if any of his children is a boy who was born on a tuesday. The man says yes. What is the probability both his children are boys?"

A riddle my brother gave me today

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