# Family with a daugter/odds they have a son **URL:** \ **Category:** Cecil's Columns/Staff Reports\ **Created:** [September 12, 2013, 1:44am UTC](https://boards.straightdope.com/t/family-with-a-daugter-odds-they-have-a-son/668626 "2013-09-12T01:44:12Z")\ **Posts on this page:** 7\ **Page:** 4
**Author:** ![Skinny](https://avatars.discourse-cdn.com/v4/letter/s/9f8e36/32.png) [@Skinny](https://boards.straightdope.com/u/Skinny)\ **Post date:** [September 13, 2013, 8:46pm UTC](https://boards.straightdope.com/t/family-with-a-daugter-odds-they-have-a-son/668626/61 "2013-09-13T20:46:27Z")
Thanks for all the replies to my original post. With your help, and my own counter productive thoughts while at work, I’ve come to understand the answer is 2/3. The idea that the smallest information changes the probability is quite annoying to the real world brain, the phrasing is just right to provoke a quick (wrong) answer. Adding any identifying aspect to the female child makes it 50%. It doesn’t change the real world chance of either child, just the theoretical probability we can expect from the information we have. Ugh. ---
**Author:** ![Powers](https://avatars.discourse-cdn.com/v4/letter/p/edb3f5/32.png) [@Powers](https://boards.straightdope.com/u/Powers)\ **Post date:** [September 13, 2013, 8:47pm UTC](https://boards.straightdope.com/t/family-with-a-daugter-odds-they-have-a-son/668626/62 "2013-09-13T20:47:36Z")
> [@Heart\_of\_Dorkness](#): > > Okay, I see the problem. We are posing two different questions. The only thing you changed was “my other child” to “Claire’s sibling”. The two are synonymous, so that change cannot affect the logic of the question in any way. You’re just interpreting the same question two different ways. Of course, your first way is wrong. Here’s the confusion: birth order doesn’t matter any more, because what we’re specifying about the child is not whether she’s older or younger but rather what she’s doing tomorrow. So the full universe of possibilities is as follows: 1. Partying girl, no-party girl 2. Partying girl, no-party boy 3. Partying boy, no-party girl 4. Partying boy, no-party boy Each is equally likely, and we’ve eliminated 3 and 4, leaving just 1 and 2. So the answer is 1/2. (Note that if we assume that /both/ kids could be going to a slumber party, then your answer of 2/3 is correct. But then it’s just as correct for the second question as well.) Powers &8^] ---
**Author:** ![bup](https://avatars.discourse-cdn.com/v4/letter/b/6bbea6/32.png) [@bup](https://boards.straightdope.com/u/bup)\ **Post date:** [September 13, 2013, 9:31pm UTC](https://boards.straightdope.com/t/family-with-a-daugter-odds-they-have-a-son/668626/63 "2013-09-13T21:31:44Z")
This problem comes up from time to time. Here’s a [previous thread.](http://boards.straightdope.com/sdmb/showthread.php?t=548215) And [here’s a poll](http://boards.straightdope.com/sdmb/showthread.php?t=548550) that the previous thread spawned. ---
**Author:** ![Heart\_of\_Dorkness](https://avatars.discourse-cdn.com/v4/letter/h/4bbf92/32.png) [@Heart\_of\_Dorkness](https://boards.straightdope.com/u/Heart_of_Dorkness)\ **Post date:** [September 13, 2013, 9:42pm UTC](https://boards.straightdope.com/t/family-with-a-daugter-odds-they-have-a-son/668626/64 "2013-09-13T21:42:47Z")
> [@Powers](#): > > The only thing you changed was “my other child” to “Claire’s sibling”. The two are synonymous, so that change cannot affect the logic of the question in any way. You’re just interpreting the same question two different ways. Of course, your first way is wrong. No, “my other child” refers to one of two children _in a family_. The units being discussed are _families_, and the specific universe of families being discussed is _those with two children, one of whom is a girl_. “Claire’s sibling” refers to a child who is the sibling of _a girl_. The units being discussed are _girls_, and the specific universe of girls being discussed is _those with one sibling_. Yes, I’m interpreting the question two different ways. That was precisely my point. But neither interpretation is wrong. The coworker says, “I have two kids.” Later he says, “My daughter Claire is going to a slumber party this weekend.” And then someone asks you, “Hey, coworker mentioned a daughter; what are the odds that his other kid is a son?” One way to phrase the question is, “In my coworker’s family, which has two kids, one is a girl. What are the odds the other is a boy?” So, we look at all the families with two kids (four kinds): Girl A and Boy A Boy B and Girl B Girl C and Girl D Boy C and Boy D We eliminate the families with no girls (one kind): Girl A and Boy A Boy B and Girl B Girl C and Girl D [del]Boy C and Boy D[/del] We look at the remaining families with boys (2 kinds) **Girl A and Boy A Boy B and Girl B** Girl C and Girl D [del]Boy C and Boy D[/del] And without (1 kind) **Girl A and Boy A Boy B and Girl B** _Girl C and Girl D_ [del]Boy C and Boy D[/del] And we figure the odds that this family with a girl also has a boy: 2/3. And we completely ignore the fact that the daughter is named Claire, or that she even has a name, because we’re not talking about girls, we’re still talking about families. The only reason her name was even of interest is that it accompanied the fact that one of the family’s two children is a girl. Another way to interpret it is, “My coworker has a daughter, Claire. He has two kids, so therefore, she has a sibling. What are the odds her sibling is a boy?” So, we look at all the girls with siblings (4 kinds) Girl A and Boy A Boy B and Girl B Girl C and Girl D We count those with boy siblings (2 kinds) **Girl A** and Boy A Boy B and **Girl B** Girl C and Girl D And those without (2 kinds) **Girl A** and Boy A Boy B and **Girl B** _Girl C_ and _Girl D_ And we figure the odds that this girl Claire has a brother: 1/2. And the only reason her name or her plans or any of those other details are relevant is because now we’re not talking about families, we’re talking about girls like Claire. ---
**Author:** ![Irishman](https://avatars.discourse-cdn.com/v4/letter/i/b487fb/32.png) [@Irishman](https://boards.straightdope.com/u/Irishman)\ **Post date:** [September 13, 2013, 9:42pm UTC](https://boards.straightdope.com/t/family-with-a-daugter-odds-they-have-a-son/668626/65 "2013-09-13T21:42:51Z")
> [@Heart\_of\_Dorkness](#): > > I read this as the coworker saying, “I have two kids. One is a daughter. Her name is Claire, incidentally, and she’s going to a slumber party. What are the odds that my other kid is a boy?” The answer is 2/3. Knowing other information about that daughter is completely irrelevant _unless_ it alters the universe in question: families with two kids, one of which is a girl. Knowing the girl’s name or her weekend plans does not change the universe. I don’t see how you can say anything about one of the children and not change the universe. You have changed the statement from “one of my children is a girl” to “this child is a girl”. Which child? Claire, or the one going to a sleepover, or the one wearing pigtails, or whatever additional information was provided. But I agree with your explanation of the outcomes for the different perspectives. ---
**Author:** ![Powers](https://avatars.discourse-cdn.com/v4/letter/p/edb3f5/32.png) [@Powers](https://boards.straightdope.com/u/Powers)\ **Post date:** [September 14, 2013, 2:45pm UTC](https://boards.straightdope.com/t/family-with-a-daugter-odds-they-have-a-son/668626/66 "2013-09-14T14:45:30Z")
> [@Heart\_of\_Dorkness](#): > > No, “my other child” refers to one of two children _in a family_. The units being discussed are _families_, and the specific universe of families being discussed is _those with two children, one of whom is a girl_. > > “Claire’s sibling” refers to a child who is the sibling of _a girl_. The units being discussed are _girls_, and the specific universe of girls being discussed is _those with one sibling_. > > Yes, I’m interpreting the question two different ways. That was precisely my point. But neither interpretation is wrong. Okay, I see now… but what you’re missing is that it’s not the wording of the sibling-referrent (“my other child” versus “Claire’s sibling”) that limits the universe and results in the 1/2 probability; it’s the _identification of Claire_. The sibling and how you refer to him/her has nothing to do with it; it’s entirely about Claire. You’re getting the right result in the second case, but the wrong one in the first case because you’re paying attention to the wrong thing. In the first case, the universe of families being discussed is not _those with two children, one of whom is a girl_, it’s _those with two children, a girl named Claire and another one_. That universe is identical to the one of _girls named Claire with one sibling_. Powers &8^] ---
**Author:** ![Irishman](https://avatars.discourse-cdn.com/v4/letter/i/b487fb/32.png) [@Irishman](https://boards.straightdope.com/u/Irishman)\ **Post date:** [September 16, 2013, 8:43pm UTC](https://boards.straightdope.com/t/family-with-a-daugter-odds-they-have-a-son/668626/67 "2013-09-16T20:43:13Z")
> [@Heart\_of\_Dorkness](#): > > The coworker says, “I have two kids.” Later he says, “My daughter Claire is going to a slumber party this weekend.” And then someone asks you, “Hey, coworker mentioned a daughter; what are the odds that his other kid is a son?” Here is the problem in a nutshell. By stating “other kid” in that question, you have to look at what is meant by “other”. In this case, other than the specified kid, the daughter, Claire, who is going to a slumber party. Whether you know her name is Claire, or only know she is going to a slumber party, you have specified a kid. So you can only look at the _other_ kid, i.e. the “not-Claire” kid or the “not going to the sleepover” kid. [Previous page](https://boards.straightdope.com/t/family-with-a-daugter-odds-they-have-a-son/668626.md?page=3)