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Thread: Birthday Cake

  1. #1 Birthday Cake 
    Time Lord zinjanthropos's Avatar
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    I was just reading something about Richard Dawkins and discovered that we share the same birthdate. Not the year but day of the month. I went googling and found out we also share the same birhday as Leonard Nimoy.

    I also remember reading an article several years ago about how many people you would need in a room before you could find two people with the same birthday. Surprisingly it is not 365. However I've forgotten the exact number. Does anyone know or even have heard of this before? And just for grins, who do you share a birthday with?


    All that belongs to human understanding, in this deep ignorance and obscurity, is to be skeptical, or at least cautious; and not to admit of any hypothesis, whatsoever; much less, of any which is supported by no appearance of probability...Hume
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    Forum Bachelors Degree Demen Tolden's Avatar
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    Wouldn't the answer be 2? I don't think you could go any lower than that.


    The most important thing I have learned about the internet is that it needs lot more kindness and patience.
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    Forum Bachelors Degree Demen Tolden's Avatar
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    And I am proud to say that I share a birthday with Mister William H Bonny himself. That old regulator standing up for the murder of his friends, fighting against those dirty merchants in a land with no real government.

    Ah, the Lincoln County Cattle War, great story.

    I say no real government even though I know there was an "official" government, I just mean it wasn't much of a government.
    The most important thing I have learned about the internet is that it needs lot more kindness and patience.
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    Moderator Moderator AlexP's Avatar
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    Quote Originally Posted by Demen Tolden
    Wouldn't the answer be 2? I don't think you could go any lower than that.
    Kind of depends on how you interpret the question, but I agree, 2 is a good answer.
    "There is a kind of lazy pleasure in useless and out-of-the-way erudition." -Jorge Luis Borges
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    You still need 366 people if you want to make sure there are two people with the same birthday, but the break even point is around 23 and it is almost a certainty when you get to about 57 or more. This refers to the probability that any two people in a room share a birthday, not that somebody else has the same birthday as you.
    http://en.wikipedia.org/wiki/Birthday_paradox
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  7. #6  
    Forum Professor Obviously's Avatar
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    My birthday is today, fancy that!
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  8. #7  
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    Happy birthday,

    If I still had any power in this place I'd send you a cut of the takings!
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  9. #8  
    Forum Professor Obviously's Avatar
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    Thanks^^
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  10. #9 Re: Birthday Cake 
    Forum Professor sunshinewarrior's Avatar
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    Quote Originally Posted by zinjanthropos

    I also remember reading an article several years ago about how many people you would need in a room before you could find two people with the same birthday. Surprisingly it is not 365. However I've forgotten the exact number.
    Hey Zinj

    Harold gave you the number. If you're interested in the calculation, here's how it goes:

    1. For any two people, taken randomly, the chance that they share a birthday is 1/365 (whatever the birthday of one, there are 364 ways in which the other can be different). So the chance they don't share a birthday is 364/365 (we're ignoring Leap Years here).

    2. For three people, therefore, the chance they don't have a shared birthday between them is (364/365) x (363/365)

    3. As the number of people increases, the chance of none of them sharing a birthday correspondingly decreases: (364/365) x (363/365) x (362/365) x (361/365)...

    4. By the time you have 23 people together, the chance of none of them sharing a birthday is therefore approximately(and I've done the calculations for you): 0.492702766, or less than 50%. Or, as the counter-intuitive initial 'problem' suggests, there is a better than half chance that, in a room of 23 randomly selected people, at least two will share a birthday.

    5. Harold suggests a near certainty by the 57th person mark. Well, he's right of course: 0.009877541 is the chance that no two people share a birthday in those circumstances, so the chance of at least two of the people being born on the same day is just over 99%!

    6. You can see from the workings that this goes back to standard permutations and combinations theory and you should be able to devise a general equation (obviously involving factorials!) that gives the result for any such event for any group size (even if the limiting factor is not the number of days in the year). :P

    Hope this helps.

    cheer

    shanks
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    The Doctor Quantime's Avatar
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    Happy birthday Obviously .
    "If you wish to make an apple pie from scratch, you must first invent the universe". - Carl Sagan
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    Quote Originally Posted by svwillmer
    Happy birthday Obviously .
    Thank you^^
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    Forum Bachelors Degree Shaderwolf's Avatar
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    Happy birthday to you...ect.
    I want to see the presents!
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  14. #13  
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    Now come on get back to the science otherwise I'm gonna lock thi.. err forget that chaps...
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  15. #14  
    Forum Bachelors Degree Shaderwolf's Avatar
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    sorry
    What a hypocrite I am!
    I was just posting something relevant to the topic

    Now, back to the science section...
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  16. #15  
    Time Lord zinjanthropos's Avatar
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    Thanks to Harold and Sunshine. When I went to bed last nite I knew 365 needed to be at least one more and 2 more in a leap year. My mistake. I knew the answer wasn't 366 or 367.

    Thinking leap year baby here now. A person born on Feb 29. So along the same lines....Would the number of people required in the room be the same if the situation was for two people born on Feb 29 to be there.
    All that belongs to human understanding, in this deep ignorance and obscurity, is to be skeptical, or at least cautious; and not to admit of any hypothesis, whatsoever; much less, of any which is supported by no appearance of probability...Hume
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    Quote Originally Posted by zinjanthropos
    Thanks to Harold and Sunshine. When I went to bed last nite I knew 365 needed to be at least one more and 2 more in a leap year. My mistake. I knew the answer wasn't 366 or 367.

    Thinking leap year baby here now. A person born on Feb 29. So along the same lines....Would the number of people required in the room be the same if the situation was for two people born on Feb 29 to be there.
    I wasn't even thinking of leap year. If there were 365 possible birthdays, and there are 365 people in the room, they could each have a different birthday, then you would need 1 more to make it a dead certainty, hence why I said 366. Now, considering Feb. 29 that would make it 367.

    That calculation we were referring to was the probability of any two people in the room having the same birthday, not a date specified in advance. It would be thrown off some by the Feb. 29 possibility, but not by much. That date would complicate things because it is only 1/4 as likely as the others.
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  18. #17  
    Time Lord zinjanthropos's Avatar
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    Quote Originally Posted by Harold14370
    I wasn't even thinking of leap year. If there were 365 possible birthdays, and there are 365 people in the room, they could each have a different birthday, then you would need 1 more to make it a dead certainty, hence why I said 366. Now, considering Feb. 29 that would make it 367.

    That calculation we were referring to was the probability of any two people in the room having the same birthday, not a date specified in advance. It would be thrown off some by the Feb. 29 possibility, but not by much. That date would complicate things because it is only 1/4 as likely as the others.
    I think that Feb 29 would be just another date on the calendar regardless of the fact it occurs every 4 years. If we are talking about shared birthdays in a room of people then I think it would be included with the other 365 days.. Should Sunshine's calculations reflect the 366?
    All that belongs to human understanding, in this deep ignorance and obscurity, is to be skeptical, or at least cautious; and not to admit of any hypothesis, whatsoever; much less, of any which is supported by no appearance of probability...Hume
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  19. #18  
    Forum Freshman teeniewitabeenie1's Avatar
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    chocolate angel cake with vanilla icing and rainbow sprinkles!!!
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