It’s kind of an unfair question though. This question hinges upon two things: You’re expected to use your knowledge of days-of-the-week, but *also* expected to _ignore_ your knowledge that boys are not always born on Wednesdays. Hence, many people will give wrong answers of 1/2 or 1/3 (perhaps recalling Monty Hall type questions). As soon as I saw “probability” I suspected bayesian but that’s also why I didn’t answer for without knowing whether we were in “this Universe” where babies can be born on any day of the week, or a *special Universe* created by this question, where boy babies are ONLY born on Wednesdays. I’m not being pedantic: I used to work with business customers who loaded assumptions into requests and if I didn’t STOP and tease out more specificity from them, time would get wasted in giving results that were correct to the request ASKED but not to the request “meant”.

 It’s kind of an unfair question though.
 
This question hinges upon two things: You’re expected to use your knowledge of days-of-the-week, but *also* expected to _ignore_ your knowledge that boys are not always born on Wednesdays.
 
Hence, many people will give wrong answers of 1/2 or 1/3 (perhaps recalling Monty Hall type questions).
 
As soon as I saw “probability” I suspected bayesian but that’s also why I didn’t answer for without knowing whether we were in “this Universe” where babies can be born on any day of the week, or a *special Universe* created by this question, where boy babies are ONLY born on Wednesdays.
 
I’m not being pedantic: I used to work with business customers who loaded assumptions into requests and if I didn’t STOP and tease out more specificity from them, time would get wasted in giving results that were correct to the request ASKED but not to the request “meant”.
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 But the wording of the question is misleading as cultural knowledge is BOTH expected to be included (7 days in a week) and ALSO ignored (everybody knows babies aren’t always born on wednesdays”)
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In short the question is a con.
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  I’ll also add here: These kinds of questions are what made me realize in middle school that the people who come up with standardized test questions are sadistic adults who hate children and want them to fail. I did very well on those tests but I saw my normal classmates struggle.
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 George has two children. One of them is a boy born on a Wednesday. What’s the probability that the other child is also a boy?”Normal person reading that says: “So what if one of them was born on a Wednesday”?
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  These are the kinds of questions that cause students to hate school, distrust academia, not want to finish college and become long distance truck drivers to get as far away as possible from these games.
Just sayin’.
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  “Authority is going to trick you. Don’t trust authority because they will lie and mislead you.”Do you know that in merit tests, when you LEAVE academia, they actually try to prompt you to answer correctly? This took me a VERY long time to figure out.I’d take a test as an adult,always looking for “What’s the trick here? There’s always a trick?” and come to find that no, there’s no trick. It’s straightforward and is just testing that you generally understand what’s going on.My nephew’s 12 and since he was 8, he’s been complaining to me about the same things *I* complained about at his age and still do. These tricks, or the incomplete homework questions, or poorly worded questions on tests or badly written instructions.It’s an epidemic in academia, a cycle of abuse going back generations and it must be stopped. You can help.
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  The original question did not ask if the 2nd child was born on a Wednesday as well.
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The day of the week a boy is born on is random unless labor is induced. This is cultural knowledge.
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  I know Bayes and figured it was heading that way. Not my first rodeo.It’s a poorly worded question, even as a “trick question”.
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  “Everything is a trick. Trust no authority” That’s the lesson I learned from teachers who use your ways, which, btw, is all of them just about.It’s why I don’t trust any politician, business person, marketing, or media. It’s a common GenX trait apparently, as “make nothing rote” was all the rage in 80s elementary / middle/ high / college education.Maybe that’s a good lesson. Served me well. Defined a generation who generally stays out of authority roles, preferring to be good parents and good people instead, leaving authority to the boomers and millennials.
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  You should see my nephew’s Pearrson Common Core materials and teacher made stuff. Same stuff.His lesson? Adults are incompetent sycophants and kids are smarter. School is just something to get beyond as fast as possible.
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  It’s a shame as he’s in accelerated classes and is poised for early college (take 1st two yrs community in 11th/12th grade).But his 6th grade and early 7th grade class homework was stuff like this, awkwardly written, confusing, not sure if clever or incompetent. Now all he wants is electives for slack off time and as accelerated classes take away electives, he’ll probably not finish Cambridge.Your question is but one of thousands that are alike. Word it better. It’s demoralizing.
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 Some teachers don’t like to learn. They can be the worst kind of students.
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 I understood the point. I knew it was a trick, likely leading to Bayes. I didn’t answer because of its absurdity.
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The point is to get them to think properly and analyse the question. If they’re upset that they interpreted it wrong then they should get out of the classroom because failure, repeated and miserable failure, is the only way to learn
  “failure, repeated and miserable failure, is the only way to learn.”
Oh, “Grit” teaches something. It’s all the rage right now. But WHAT students learn isn’t usually what is taught.
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Oh I understood it, Michael. I explicitly asked for a rephrasing to point out publicly the absurdity of the original question to you and everybody else here as a show of support for those who answered REASONABLY but were considered foolish.
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  I’m 46. I’m helped hundreds of kids and adults through stuff like this. I know how it works and the tricks.You don’t understand why so many consistently give similar answers. It’s due to a poor question and not a reflection of their intellectual capacity.
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  Your question gives explicit information.
To answer requires implicit knowledge.
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  In what world does the day a boy is born on have any bearing on the day of birth of another child?
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 Using Bayes rule lets us write this asP(BB | B born on Wednesday) = P( B born on Wednesday | BB) • P(BB) / P(B born on Wednesday).Calculating each term:P( B born on Wednesday | BB) is the probability that at least one of the children is a boy is born on Wednesday conditioned on the fact that both are boys. “Implied is the belief of importance of being born on a Wednesday. I knew I’d seen this before : https://www.cut-the-knot.org/Prob…/BearBornOnTuesday.shtml – and I didn’t like it then either. You MUST believe that Wednesday is an important fact to get to your answer.Bayes is extremely useful but has fundamental shortcomings. In this case, it’s measuring confidence, giving equal weigh to every ‘fact’. Boy. Wednesday. Other boy. All mathematically equal. Closed universe situation.
I know this is the nature of thought experiments and it’s unlikely the tradition isn’t ending anytime soon.
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  In short, someone who believes the first boy being born on a Wednesday has a bearing on the sex of the other child will give it a slightly lower than 50% probability rating.
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  Bayes is murky. Probability curve can be due to overconfidence (“It matters that the first boy was born in a Wednesday!”) and including it in the calculations or it can be due to taking in all possible variables and narrowing down to a conclusion that way.I’d say that overconfidence is the biggest flaw with Bayes.
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It’s the framing of a belief though.
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Is it not measuring superstition?
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  I’m given “on a Wednesday” in the phrasing.
I cannot discard this information.
This means I must accept it as equally important to all other facts in the question.
It is a measurement of superstition, that all facts equally matter, no matter how absurd. I then input these into my calculation blindly.
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  [I was “Excel guru” at a pharma once and you wouldn’t BELIEVE’ the kinds of shit they had me stick in to the calculations to show Growth and ROI.I felt dirty some days]

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  It just gets REALLY wonky at times. Once (this is back in 99-02 era) they gave me a CD-ROM full of data they snuck out of a marketing seminar from another company. Info I wasn’t supposed to have.

It was sentiments. 80 chars or less. Using Excel and VBA (and no training as I don’t think sentiment analysis was a thing that I knew of at least), I had to figure out how to parse this stuff – and I’m a stickler on some things, assign it a sentiment, give it a value and it was figured into the ROI by translating sentiment into % growth + $$$’s using an internal set of metrics some middle mgr sitting at his desk dreamt up..

Parsing was fun to figure out and I enjoyed the project but I also knew it was full of shit. All my calculations were good and solid but the whole thing amounted to a trick.

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