Monday, November 13, 2006
AAAGGGHH High School Nightmares Return
You know, I never was good at science. Not in high school. Not in college. And I'm reliving my biology nightmares with the twins. Seems they have an enthusiastic teacher who likes kids and loves science, but can't teach it. I've had a conference, asked for tips, pointers (the teacher's edition even!) but no luck. We've tried asking questions in class, going for extra help in homeroom, and IMing our friends to finish the homework. So tonight I'm sweating through Mendel and the laws of separation of chromosomes through meiosis or something like that. Why does CP live on the other side of the country??!! Somebody help me here! Even Google let me down. I can't even pretend to like this stuff. With Shakespeare I'm the hero - give me Caesar and I'll show them how Shakespeare is funny and wittily says "cry me a river." I can interpret deeper meanings in various literature. I know topic sentences. Heck I can even explain the finer points of direct and indirect objects. But don't ask me to figure out the probabilities of a family having three daughters!! It's all Greek to me...
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Clearly the probability of having 3 girls is pretty high in this cousin's little branch of the family, given that 3 of the 5 of us had multiple girls, two with 3 or more....
In the absence of other information and making the implied simplifying assumptions, it's just a simple probability problem. Assume equal odds of either girls or boys for each conception (not quite true though, as seen in our branches of the family -- are they compensating for that?), so it's the probably of one particular outcome (GGG) over the total number of possibilities. AKA, 1/(2X2x2) = 1/8.
"In the absence of more information" of course, means that the real answer to the problem stated is "not enough information." For example, the probability of having 3 girls is precisely 0 for families with 0, 1, or 2 kids. It's also different for families whose children are adopted (especially for international adoptions from certain countries).
And of course, the odds of having 3 girls is greater for families with more than 3 biological children. There are 16 combinations for families with 4 kids. Assuming precisely 3 girls, you get the following combinations of kids: BGGG, GBGG, GGBG, GGGB. So that would mean that the odds are 4/16 or 1/4. If you add in the other possibility (4 girls), you get 5/16.
The odds go up again with 5 children, and again with 6 children. Exact odds (and the trends behind them -- fun with combinatorics and probability! All the world's a math problem!) are left as an exercise to the reader.
See? It's all very simple and straightforward. Unlike weird poetry where the cloud is a metaphor for our befuddled approach to death, sometimes luminescent, sometimes opaque, sometimes sliding between us and the sun and streaming its glories. OK, I just made that up off the top of my head, but I'd bet there're plenty o' bad poems out there that use precisely that metaphor.
AFA meiosis, mitosis, recombinant dna, etc., I wasn't big on life sciences after suffering through Mr. "pick'em and fling'em"'s class in 7th grade. As DF can attest, he used to pick his elbow calluses and toss 'em at people in class while lecturing in a monotone. That turned me off of life sciences right quick. It's all nice and logical though.
But as I've learned from suffering through our school district's awful math curriculum, it all comes down to the curriculum and the way it's taught... So you can steal my kabamabooms if you'd like
Yeah...what SHE said. LOL. Being a science geek who couldn't do math, I can help ya with meiosis, mitosis, and if it is early enough in the a.m....halitosis....but beyond that, ....I will be hanging with the metaphors between the clouds where it is nice and warm.
OK, can we set up web tutoring or something? The full question (I think) was if a family is going to have 3 kids, what are the probabilties that all 3 will be girls. Austin said 1 in 4, given the choices are ggg, GGB, GBB,BBB. Shannon did something like a flow chart and got 1/8 I think. Austin's made sense to me. Then the follow up was, if you have 2 girls, what's the chances the 3rd will be a girl? I said 50%. But I think somewhere there's something about men genetically carrying more girl makers or boy makers (case in point, your brothers).
The real kicker is I emailed the teacher today to tell her how lost we all were last night, and she said, "You were supposed to be." She wanted the kids to read the next-to-impossible-to-understand text, try to answer the questions, then come to class totally confused so that she could give them 2 handouts and teach them. The problem with this idea - while good to make the kids think on their own - is that S is so totally frustrated with bio that she's convinced she is science stupid and entered class today figuring "what's the point?!" For 5 years we worked on "math esteem." Now I have to switch to "science esteem" and build up what the teacher is destroying (we finally got an awesome math teacher this year!).
Anyway, I'll be calling the two of you!!!
Heh, that's the approach my kids' school math curriculum uses. I teach them real math at home because they don't learn much at school... KABAMABOOOOOOOOOOM! (the frequent sound of my head exploding...)
If you know that 2 children are girls, what are the odds that the third is a girl? What you need to do is look at the number of combinations with two girls:
GGB, GBG, GGG, BGG.
Looks to me like GGG is 1/4. Adding more knowledge (the oldest is a girl, the middle is a girl, etc.) changes the probabilities, as you can see.
This is all math, of course. But math is a science, dontcha know.
Whoops, lunch just beeped in the microwave. Time to head back to real work...
You'd think being a lawyer I could word things better - the question was if the first two are girls, what are the odds that the third child will be a girl.
And I agree science is math, which is probably why I hate both. I was ok with math when it was just numbers, but when it started getting funky around 7th grade, I tanked. I still can't figure out how I managed to receive an economics degree, which is primarily math, too. Thank goodness there was no math in law school (except tax class, which I ultimately took "pass/fail.")
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