Welcome guest, is this your first visit? Create Account now to join.
  • Login:

Welcome to the Online Debate Network.

If this is your first visit, be sure to check out the FAQ by clicking the link above. You may have to register before you can post: click the register link above to proceed.

Results 1 to 4 of 4

Thread: Birthday Wager

  1. #1
    ODN Community Regular

    Join Date
    Sep 2004
    Location
    Palace of Kubla Khan and bovine worshippers
    Posts
    3,011
    Post Thanks / Like

    Birthday Wager

    OK, from our request line we had Kneeless call in, so this one goes out to you... (by the way, your Avatar is very mesmerizing -- I think it must represent some part of the id)
    ____________________________________

    The Problem:
    There are 250 people at a wedding. The groom is feeling lucky, and bets his best man $1000 that nobody else at the wedding has the same birthday as the best man, which happens to be August 25th, 1970. Any year with that month and day is an acceptable match.

    The groom knows only his own birthday, the best man's, the bride's, and his mother's, who is in attendance as well, and none of them are the same as the best man's, which fact the groom reveals to the best man out of courtesy. The best man does not know anyone else's birthday who's there.

    The groom asks the crowd if anyone in attendance was born on February 29th, and no one was. Everyone is accounted for, and so February 29th is eliminated.

    The current date is February 28th, 2003. The groom knows that there are two babies at the wedding less than six months old, and no one else is under two years old.

    The Object:
    Describe specifically how the groom can ensure that he will have better than even odds of winning the bet straight up as stipulated, without him or anyone else lying, cheating, being misleading, communicating with anyone else, or relying on any additional information.

    (if you have questions of clarification, please feel free to ask me)

  2. #2
    Registered User

    Join Date
    Mar 2004
    Location
    Southern California
    Posts
    1,027
    Post Thanks / Like

    Re: Birthday Wager

    ~ Most of the riddle is a red herring.
    In any group of 250 persons of random birthdate, the probability that a given birthdate will not be represented in the group is greater than 50%.
    Specifically, it is (364/365)^n where n is the number of persons (discounting Feb 29 birthdates which only increases the probability anyway.) ~
    Last edited by Galendir; October 3rd, 2004 at 12:13 AM.

  3. #3
    Registered User
    Join Date
    Feb 2004
    Posts
    631
    Post Thanks / Like

    Re: Birthday Wager

    I lack the suffient math processing to calculate the number as small as the possibility of the date happening. But here is the "exact" probability of it, albeit it is still in equational form. (If anyone can do 0.002739726^244 tell me.)

    (244 nCr 1)((1/365)^244)((364/365)^243)

    Of course, this is using (what I believe is) called Bernoulli Process, described by the equation
    (T nCr W)((p(s))^T)((p(f))^(T-W))
    Where T is the total number of trials, W is the number of trials we want to be a sucess, p(s) is the probability of sucess, and p(f) is the probability of failure. And I believe Galedir is wrong on this one, that is, if I understand the Bernoulli process correctly, which I may not.

    EDIT: I've might've found the possiblity. (EDIT#2: This number is slightly off. I ran out of memory, so this'll have to do for now...)
    .0000000000000000000000000000000000000000000000000 000000000000000000\
    00000000000000000000000000000000000000000000000000 000000000000000000\
    00000000000000000000000000000000000000000000000000 000000000000000000\
    00000000000000000000000000000000000000000000000000 000000000000000000\
    00000000000000000000000000000000000000000000000000 000000000000000000\
    00000000000000000000000000000000000000000000000000 000000000000000000\
    00000000000000000000000000000000000000000000000000 000000000000000000\
    00000000000000000000000000000000000000000000000000 000000000000000000\
    00000000000000000000000000000000000000000000000000 000000000000000000\
    00000000000000000595708923721397836333459036231321 637480121974516627\
    77816800253351244848218585536589231704253107085998 532334085176446065\
    43964070590263859713870913363074977470000169488848 536997661615540488\
    67372335895430793927242604891639701463670893250509 605066321380438681\
    08479875570343854715412160580482260764999752830237 113278619597372985\
    67091514432155930002100019660000646191056800643247 127634554586279283\
    10806295541480736923923108203535893657171058813233 300451324284759235\
    32582749831736664760229308286653704859851056387207 208128947769987211\
    88909357511672645595084970125954374065262966986090 925685413205776215\
    11105498545009461106485991603298619274640907202467 993518974531212126\
    26650346587117716125905148602959214716038271257258 789220966753881347\
    95467963842185165589550283732720718562236874813016 338276934299311514\
    69581939939095769143712887156095933996972238299685 597973746829124237\
    54821038778583947211641951022596920024688858854842 411217120007529761\
    68080517700890611107049140408609445420386204792515 840710054911739799\
    04433732275853235372305545889423994434347253448382 904988199727936955\
    78281634666882117254522783219428770688471533385454 999878673653414333\
    50282626807056341274614971715987504040026123109638 419067348488643760\
    52519469459563593900397554154341921345401042599547 689485551328769382\
    26387893079593578921895849638523679835442122248104 721135167628449515\
    11362598683124558403510374420814255524499452803580 255314287463609655\
    70550315471493872521220931378496861902654122890049 709037754668798454\
    84357512620920844314651508655494708602873893796751 721240038831587983\
    600568554921598272689696967413943446899636830208
    Last edited by KneeLess; October 3rd, 2004 at 05:21 PM.
    "The essential act of war is destruction, not necessarily of human lives, but of the products of human labour. War is a way of shattering to pieces, or pouring into the stratosphere, or sinking in the depths of the sea, materials which might otherwise be used to make the masses too comfortable, and hence, in the long run, too intelligent." 1984, By George Orwell. Part 2: Chapter 9.

  4. #4
    ODN Community Regular

    Join Date
    Sep 2004
    Location
    Palace of Kubla Khan and bovine worshippers
    Posts
    3,011
    Post Thanks / Like

    Re: Birthday Wager

    Kneeless, I'm not sure how to assess your equations, as I only made it to high school calculus. I thought Bernoulli was a race car driver. But you do get extra credit for all the extra digits.

    Galendir is correct... Give that water buffalo a cigar! I can see I'll need to pose a puzzle that does not involve probability next time.


    You have better than a 50% chance of no matching birthdays to a given birthday up to 252 people. (discounting Feb. 29)

    One thing I was curious about was the possible occurrences of twins and triplets, and if this would have any bearing on the probability. For example, if you take a random person from the crowd, what's the probability first that they are a twin? And then you have to look at the probability that their twin would also be at the same social event.

 

 

Similar Threads

  1. Birthday Theory
    By Anywien in forum General Debate
    Replies: 4
    Last Post: August 8th, 2004, 02:18 AM
  2. Happy Birthday Slipnish!!!
    By tinkerbell in forum Shootin' the Breeze / Off-Topic
    Replies: 7
    Last Post: August 3rd, 2004, 04:28 PM
  3. Happy Birthday Mrs Innocent!!
    By Dionysus in forum Shootin' the Breeze / Off-Topic
    Replies: 9
    Last Post: August 3rd, 2004, 12:42 PM
  4. In honor of Boogers birthday 7/24
    By tinkerbell in forum Shootin' the Breeze / Off-Topic
    Replies: 9
    Last Post: July 24th, 2004, 03:37 PM

Bookmarks

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •