Notices
Results 1 to 6 of 6

Thread: Percentage Probability

  1. #1 Percentage Probability 
    Forum Senior Booms's Avatar
    Join Date
    Sep 2008
    Location
    The perceptual schematic known as earth
    Posts
    361
    I saw a program talking about something or other

    what caught my attention was a proof of probability experiment;

    40 people (or so) were stopped in the street at random and asked the date they were born. The idea being two people with the same birthday being picked as very unlikely. there are 365 possible dates, and only 40 people.


    However it's a pair of people and the program said there was something like 800 possible pairs, making two matching dates much more likely (and there was a matching pair)


    I get this, What I don't get is the bit where it said the 800 pairs mean theres an 89% chance of a matching pair.




    The numbers are probably wrong in the description above, but my point and question still stands, how did they translate 800 possible pairs of dates into 89%?


    It's not how many questions you ask, but the answers you get - Booms

    This is the Acadamy of Science! we don't need to 'prove' anything!
    Reply With Quote  
     

  2.  
     

  3. #2  
    Forum Radioactive Isotope MagiMaster's Avatar
    Join Date
    Jul 2006
    Posts
    3,440
    The odds of a random person not having one of 30 or so birthdays is fairly high. The odds of picking 30 or 40 such people in a row is low.

    BTW, why is it so surprising that 800 pairs over 365 dates should give a high chance of a match? Although maybe I just don't understand your question.

    Anyway, you should just read the Wikipedia entry on this one. It's an old and well known exercise in probability.


    Reply With Quote  
     

  4. #3  
    Forum Senior Booms's Avatar
    Join Date
    Sep 2008
    Location
    The perceptual schematic known as earth
    Posts
    361
    I'll read that link


    btw, the high probability isn't what bothered me, it's how they got that number.

    In my head, 800 chances means 800 1/365ths
    which sums up to be about 2, so there should be a roughly 50% chance. I just don't see where the 80% came from
    It's not how many questions you ask, but the answers you get - Booms

    This is the Acadamy of Science! we don't need to 'prove' anything!
    Reply With Quote  
     

  5. #4  
    Forum Ph.D. Leszek Luchowski's Avatar
    Join Date
    Jun 2008
    Location
    Gliwice, Poland
    Posts
    807
    Quote Originally Posted by Booms
    In my head, 800 chances means 800 1/365ths
    which sums up to be about 2, so there should be a roughly 50% chance.
    Three wrongs don't make a right.

    First wrong: You try to get the overall probability of something happening at least once in many tries by adding the probabilities in each try.

    This gave you a probability roughly equal to 2. You instinctly balked at it and, in a rather random attempt to correct this, committed

    Second wrong: You took the inverse of that number 2, for no other reason than that it gave a plausible result (between 0 and 1).


    Just think of this: if the number of people is increased, your sum will increase accordingly, and its inverse (which you take for the probability you are looking for) will decrease. This just cannot be so.


    Third wrong: You took it that 800 people mean 800 tries, each with 1/365 chances of success. In fact, 800 people mean possible pairs, each with 1/365 chance.

    Hope this helps. No time to propose a correct solution now.
    Leszek. Pronounced [LEH-sheck]. The wondering Slav.
    History teaches us that we don't learn from history.
    Reply With Quote  
     

  6. #5  
    Forum Radioactive Isotope MagiMaster's Avatar
    Join Date
    Jul 2006
    Posts
    3,440
    It was 40 people, giving pairs, so 780, or about 800.

    But yeah, the rest is still true.

    Booms, when you have a series of events, you can't simply add the probabilities. If you have a sequence of events with probability p (say ), the chance of that event failing n times is the same as the chance of it not happening (1-p) every time (), which for n = 780, gives , which gives the chances of it happening at least once as 1 - that, or 0.882.

    Now, I think that's only an approximation of the actual probability, since after 365 people, you'd be guaranteed to find a match, but that probability would still be (slightly) less than 1.

    To get the actual probability, first ask what chance is there that two people have different birthdays (364/365). Then add a third person. What is the chance that they have a different birthday (363/365). Then a fourth (362/265). After 40, what's the final chance that they're all different (364/365 * 363/365 * 362/365 * ...). Then 1 - that for the chance of a match.

    I get about .891 for that. So the approximation by the number of pairs is pretty close, but not perfect.
    Reply With Quote  
     

  7. #6  
    Forum Senior Booms's Avatar
    Join Date
    Sep 2008
    Location
    The perceptual schematic known as earth
    Posts
    361
    ah many thanks
    It's not how many questions you ask, but the answers you get - Booms

    This is the Acadamy of Science! we don't need to 'prove' anything!
    Reply With Quote  
     

Bookmarks
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
  •