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The Tuesday Birthday Problem 981

An anonymous reader sends in a mathematical puzzle introduced at the recent Gathering 4 Gardner, a convention of mathematicians, magicians, and puzzle enthusiasts held biannually in Atlanta. The Tuesday Birthday Problem is simply stated, but tends to mislead both intuitive and mathematically informed guesses. "I have two children, one of whom is a boy born on a Tuesday. What's the probability that my other child is a boy?" The submitter adds, "Believe it or not, the Tuesday thing is relevant. Well, sort of. It's ambiguous."
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The Tuesday Birthday Problem

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  • This reminds me of a famous joke and variations thereof, (at least around eastern europe):

    A man is asked on the street: What is the probability you will come across a dinosaur on the street today?

    The man replies: less than 0,000000001%

    When a woman is asked the same question, she replies:

    50% - I either will or I won't.

    So, really, it depends on who you ask.
  • by williamhb ( 758070 ) on Tuesday June 29, 2010 @05:36AM (#32727910) Journal

    As the article notes, it depends what you mean by "one of", (specific one vs "at least one"), and quibbling mathematicians don't always pick the most common interpretation.

    In other news, an aeroplane carrying a hundred mathematicians crashed with no survivors; their university made a press release stating that one of its mathematicians died in the crash.

  • by Anonymous Coward on Tuesday June 29, 2010 @05:52AM (#32728034)

    Yeah, but the chance of it being a girl is more than 1 in 2, it is about 51 percent, and then you have to allow for which country the kid was born in (to cater for female infanticide)... if you are being pedantic.

  • by mim ( 535591 ) on Tuesday June 29, 2010 @05:54AM (#32728044)
    I used to tend bar and this is not a math puzzle, but fun for messing with the barflies when they've had a beer or 5 and start wanting to tell you their life story. First, as you pose the question, take out 3 coins (this only translates well using USA coins, one being a nickle, the other a penny, the third a quarter, dime or fifty cent piece) and state that "Johnny's Mom has 3 kids, the first one is named 'Penny,' (point to the penny) the second one is name is 'Nicky' (point to the nickle) and then point to the third coin (doesn't matter which you use) and ask What is the third child's name?" Then see how long it takes them to figure it out. And then whether or not they leave you a tip.
  • by itsdapead ( 734413 ) on Tuesday June 29, 2010 @06:06AM (#32728108)

    Take an abstract mathematical problem, invent a pseudo-real-world context, rephrase the problem very sloppily and ambiguously in plain English then laugh smugly when people get the wrong answer.

    The correct answer to the question, by the way, is "I don't know - you have not given me enough information, and I'd have to go check that the gender of successive offspring from the same couple is actually independent, but its probably gonna be somewhere between 1/3 and 2/3 - and since you'd have to somehow re-formulate it as a viable experiment and run it 100 times to confirm that result, only the Bayesians give a flying fuck what the precise value is".

    In other news: you can't actually build a hotel with an infinite number of rooms - you'd run out of bricks - so don't try and engage my interest in all the weird thing that would happen if you did something impossible. And stop hiding goats behind my door!

  • Re:Well? (Score:2, Funny)

    by Anonymous Coward on Tuesday June 29, 2010 @06:17AM (#32728156)

    Only if you believe in randomness. If the other child in fact is a boy the probablility for it is 1.

  • by houghi ( 78078 ) on Tuesday June 29, 2010 @06:40AM (#32728262)

    If the dad is Schrödinger the other kid is both born and unborn at the same time.

  • by Asmor ( 775910 ) on Tuesday June 29, 2010 @07:16AM (#32728490) Homepage

    In other news: you can't actually build a hotel with an infinite number of rooms - you'd run out of bricks

    Don't let the venture capitalist who's funding me know that. I duped him into paying me an infinite amount of money! He paid me $1000 for the first room, $500 for the second, $250 for the third, etc. I'll be rich! Rich, I tells ya! I've been eying this nice $2000 watch, and I should have enough for it any day now...

  • by Anonymous Coward on Tuesday June 29, 2010 @07:23AM (#32728540)

    Janitor: Hey. We solved your dumb game.
    Troy: We been to the libary!
    Janitor: "-brary," Troy. "Li-BRAR-y." Anyway, "What two coins, when you put 'em together, makes thirty cents and one of them isn't a nickel?" Hmmmm. A _penny_ and...a 1972 dime with a Roosevelt imperfection, today worth exactly twenty-nine cents.
    J.D.: Nope, nope, nope. The correct answer is: A quarter and a nickel.
    Janitor: Uh, no. Because you said one of 'em _isn't_ a nickel.
    J.D.: Right. The _other one_ is.
    Janitor: You lied to me.
    J.D.: No. It's a riddle.
    Troy: Ooh! Your face is red! Like a strawbrerry!

  • by stewbacca ( 1033764 ) on Tuesday June 29, 2010 @08:17AM (#32728920)

    I have never seen "DOES not disallow" in my entire life.

    You haven't been watching the officiating during the World Cup.

    Example: "The referee does not disallow goals that are scored fairly unless they are scored by the United States."

  • Re:Well? (Score:4, Funny)

    by bsDaemon ( 87307 ) on Tuesday June 29, 2010 @09:07AM (#32729452)

    ...what that actually represents is both having one rock in your presence butt also...

    I'm sure glad I don't have a rock present in my butt...

  • Re:Well? (Score:3, Funny)

    by ticklemeozmo ( 595926 ) <justin,j,novack&acm,org> on Tuesday June 29, 2010 @09:19AM (#32729604) Homepage Journal

    My older brother and I were both born on Tuesdays.

    Nothing to see here, just a systemic anomaly. Move along, now.

  • Re:Well? (Score:4, Funny)

    by Chapter80 ( 926879 ) on Tuesday June 29, 2010 @10:02AM (#32730270)

    We can say that the boy, who was born on a tuesday, was also a Gemini. Does this change the ratio? No, the probability of having two boys is still 50-50%, because the unknown only has two possible outcomes: boy or girl.

    Did I win the lottery last week? The unknown only has two possible outcomes: I won or I lost.
    Therefore, based on your math, my odds are 50-50%.

    University of Phoenix online wants their diploma back. :-)

  • by RevWaldo ( 1186281 ) on Tuesday June 29, 2010 @11:25AM (#32731628)
    It's the 1970's. Two math professors, old friends who both live in London, are on the phone discussing an upcoming conference in Edinburgh they'll both be attending.

    - Hey, we could fly over together if you'd like.
    - Thanks, but I'll be driving.
    - All that way? It'd take you most of the day! Whatever for?
    - Well, I recently made a study of the statistics of bombs being smuggled on board passenger planes. And while the odds of it occurring on any particular flight are high, the possibility still makes me uncomfortable with flying.
    - Well, suit yourself. I'm going to take the plane.

    A short time later, the one professor is boarding her flight out to the conference, and who should be sitting in the adjacent seat but her old friend! They're both pleasantly surprised, and the first professor settles into her seat. She leans in and quietly asks her friend -

    - So what about that whole probability issue? Was your math off, or did you just work up the nerve?
    - Wrong on both counts! I did have a breakthrough, however.
    - Really? How do you mean?
    - Well, I went over the statistics again, and worked out the odds of two bombs being separately smuggled on board the same flight.
    - High?
    - Astronomical! You've a better chance of being struck by lightning!
    - So how does knowing that make you more comfortable with flying?
    - (singsongs) Guess what I've got in the briefcase...(pats the case on her lap)

  • by liam193 ( 571414 ) * on Tuesday June 29, 2010 @12:39PM (#32732646)

    I have two slashdot readers and one of them did not read the article before they posted a reply on a Tuesday. What is the probability that the other didn't read the article as well?


  • Dear /. (Score:3, Funny)

    by geekoid ( 135745 ) <dadinportland AT yahoo DOT com> on Tuesday June 29, 2010 @01:48PM (#32733750) Homepage Journal

    Can you please create a flag for everyone that posted a wrong conclusion and then filter them out of all my views in the futures.

    I wish to do this because it will eliminate people who don't read the articles and people who can't do math.

    Thank you.

User hostile.