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Topic: Birthday paradox

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Birthday

Inequality of arithmetic and geometric means

Paradox

Birthday attack

Probability

Liar paradox

Combinatorics

Cryptographic hash function

Raven paradox

Vacuous truth

Elevator paradox

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	Birthday paradox - Wikipedia, the free encyclopedia
		This is not a paradox in the sense of leading to a logical contradiction; it is a paradox in the sense that it is a mathematical truth that contradicts common intuition.
		This is exploited by birthday attacks on cryptographic hash functions and is the reason why a small quantity of collisions in a hash table are, for all practical purposes, inevitable.
		The theory behind the birthday problem was used in [Schnabel 1938] under the name of capture-recapture statistics to estimate the size of fish population in lakes.
	en.wikipedia.org /wiki/Birthday_paradox (1670 words)

	Paradox - Wikipedia, the free encyclopedia
		A paradox is an apparently true statement or group of statements that leads to a contradiction or a situation which defies intuition.
		Paradoxes that arise from apparently intelligible uses of language are often of interest to logicians and philosophers.
		Paradoxes which are not based on a hidden error generally happen at the fringes of context or language, and require extending the context or language to lose their paradox quality.
	en.wikipedia.org /wiki/Paradox (911 words)

	Illuminations: Birthday Paradox
		Students can then run calculator-based simulations of the birthday paradox and can explore the fact that more than 50 percent of the time, when groups of "random" strangers are assembled, only twenty-three persons are needed to find a matching pair of birthdays.
		For example, in the birthday paradox, a group of twenty-three randomly selected persons must be selected to have a greater than 50 percent chance that any two of them share the same birthday (Lesser, 1999).
		The probability that two strangers do not share a birthday is 364/365, assuming that neither of them was born in a leap year, with the probability of a match being the complement of this event, that is, 1 -(364/365), or.00274.
	illuminations.nctm.org /index_d.aspx?id=299 (1961 words)

	Estimating Population
		Subsequently, the classical "birthday paradox" was reversed to estimate statistical population from the average number of repetitions found in trials containing a substantial number of random samples.
		The birthday paradox has been proposed for public-key distribution in Merkle [13: 13-21], used for DES analysis in Kaliski, Rivest and Sherman [6] (also described in Patterson [17: 156-166]), and forms the basis for authentication attacks described in Seberry and Pieprzyk [21: 157].
		Birthday methods were apparently used by Letham, Hoff and Folmsbee (1986) [11] during tests of the hardware random number generator on the Intel 27916 "Keprom" (see Appendix B); results were given, but the theory of the test itself was not described.
	www.ciphersbyritter.com /ARTS/BIRTHDAY.HTM (7677 words)

	Reference.com/Encyclopedia/Birthday paradox (Site not responding. Last check: 2007-11-07)
		In his autobiography, Paul Halmos deplored the fact that the birthday paradox is often presented in terms of mere numerical computation rather than conceptual mathematics.
		The theory behind the birthday problem was used in 1938 under the name of capture-recapture statistics to estimate the size of fish population in lakes.
		The birthday problem for such non-constant birthday probabilities was tackled in 1967.
	www.reference.com /browse/wiki/Birthday_paradox (1190 words)

	The Birthday Paradox Revisited
		The Birthday Paradox is mathematically proven, so well in fact that the Birthday Attack can be used to break certain cryptographic cyphers.
		I don't see how this is a "paradox" or anything other than someone who wasn't smart enough to solve anything but the odd numbered problems in math class complaining about their stupidity.
		Birthdays may not be perfectly distributed but its not like there is any particular day that is twice as likely to have people be born on it.
	digg.com /links/The_Birthday_Paradox_Revisited (3399 words)

	First Birthday (Site not responding. Last check: 2007-11-07)
		The birthday cake is traditionally a highly decorated cake, and is typically covered with lit candles when presented; the number of candles equals the age of the person.
		A birthday attack is a type of cryptographic attack which exploits the mathematics behind the birthday paradox, making use of a space-time tradeoff.
		I think the birthday paradox is one of those problems where you have to be careful not to run into limited precision floating point problems, but I'm not sure.
	www.wwwtln.com /finance/77/first-birthday.html (1726 words)

	Math Forum: Ask Dr. Math FAQ: The Birthday Problem
		That gives him 365 possible birthdays out of 365 days, so the probability of the first person having the "right" birthday is 365/365, or 100%.
		To solve the birthday problem, we need to use one of the basic rules of probability: the sum of the probability that an event will happen and the probability that the event won't happen is always 1.
		We know that the probability of finding at least two people with the same birthday is 1 minus the probability that everybody has a different birthday, and we know how to find the probability that everybody has a different birthday for any number of people.
	mathforum.org /dr.math/faq/faq.birthdayprob.html (825 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		That's the Birthday Paradox, which answers "How many people do you need for it to be more likely than not that two share a birthday?".
		This is not a paradox in the sense of leading to a logical contradiction; it is a paradox in the sense that it is a mathematical...
		Birthday paradox: What is the chance that two people in a room have the same birthday?
	www.worldhistory.com /wiki/B/Birthday-paradox.htm (778 words)

	JFK Assassination Coincidences -- Wildly Improbable?
		And it follows that probability of A and B not having the same birthday and B and C also not having the same birthday and A and C not having the same birthday is.99726 x.99726 x.99726 = 0.9918.
		Since the number of possibilities of two people having the same birthday increases roughly as the square of the number of people, the probability of at least two having the same birthday rises rapidly as the number in the room increases.
		This is a bit of a simplification, because birthdays are not in fact randomly distributed across the 365 days of the year.
	mcadams.posc.mu.edu /logic3.htm (864 words)

	Birthday Paradox: Formula, Probability, Combinatorics
		The birthday paradox calculates that the probability to get the same pick-3 combination at least two times in 100 trials is 99.4%.
		The cold truth is that the famous and appealing Birthday Paradox merely shows the percentage of sets with duplicate elements in the total elements of an exponential set.
		The Birthday Paradox is one tiny particular case derived from the mathematical sets named EXPONENTS or Saliusian sets.
	www.saliu.com /birthday.html (4164 words)

	The Birthday Paradox Explained \| FOB
		The Birthday Paradox is a well known statement of probability: if you have 50 people in a room, almost certainly (97%) at least two of them have the same birthday.
		So it seems clear that if 130 people were in the room, two would almost certainly have the same birthday, because even if the first 120 didn't contain such a pair, one of the next 10 would.
		Since with two people in the room, there's little chance they'll have the same birthday, the number of people for which the chance of a same birthday is 50% is going to be somewhere between 2 and 120 (already less than half), but by our math it looks way closer to 2 than 120.
	fob.po8.org /node/90 (536 words)

	[No title]
		One of the most famous and relevant examples is the so-called Birthday Paradox, which states that in a random gathering of just 23 people, there are 50:50 odds that at least two of those present have the same birthday.
		If the Birthday Paradox is correct, then in a sample of F fixtures, we expect about 0.5F to contain at least one pair of players sharing the same birthday.
		This is a reflection of the fact that there is a significant preponderance of players' birthdays in November and December, and deviations away from a uniform distribution of birthdays always tend to boost still further the number of observed coincidences.
	ourworld.compuserve.com /homepages/rajm/tscoin.htm (1693 words)

	Howstuffworks "Someone told me that if there are 20 people in a room, there's a 50/50 chance that two of them will have ...
		This phenomenon actually has a name -- it is called the birthday paradox, and it turns out it is useful in several different areas (for example, cryptography and hashing algorithms).
		For example, if you meet someone randomly and ask him what his birthday is, the chance of the two of you having the same birthday is only 1/365 (0.27%).
		When you put 20 people in a room, however, the thing that changes is the fact that each of the 20 people is now asking each of the other 19 people about their birthdays.
	www.howstuffworks.com /question261.htm (430 words)

	Birthday paradox (Site not responding. Last check: 2007-11-07)
		The birthday paradox states that if there are 23 people in a room then there is a chance of more than 50% that at least two of them will have the same birthday.
		This means that a higher probability applies to a typical school class size of thirty, where the 'paradox' is often cited.
		It may be counter-intuitive to someone who does do the simple math to prove it, but it is a very simple thing to prove.
	digg.com /science/Birthday_paradox (123 words)

	THE BIRTHDAY PARADOX
		My good friend John Rensch’s son says that a paradox is a partnership of two doctors.
		Thus, for example, if it can be shown that the probability is.03 that no two people out of 50 have the same birthday--then the probability that two do is: 1 -.03 =.97 or 97%.
		And, in general, the probability that at least 2 out of n people in a given population have the same birthday is: 1 - (364/365 X 363/365 X.
	www.thestraights.com /wesfager/birthday-paradox.htm (363 words)

	Damn Interesting » The Birthday Paradox
		There is a classic cryptographic computer attack known as the "birthday attack" which exploits the math of the birthday paradox.
		But consider that the people didn't choose their birthdays - they were all picked at random from the same set of 365, not from that constrained set.
		Well, the odds of you being born on 3/13 are 1 in 365, but you walked into the room with that birthday, so it was a foregone conclusion and gave the date significance, so that much is a probability of 1.
	www.damninteresting.com /?p=402#more-402 (6698 words)

	The Birthday Paradox
		People's birthdays are equally distributed over the other 365 days of the year.
		Hence the probability that a randomly selected person was born on February 29 is 0.25/365.25, and the probability that a randomly selected person was born on another specified day is 1/365.25.
		The Birthday Paradox shows that the probability that two or more items will end up in the same bin is high even if the number of items is considerably less than the number of bins.
	efgh.com /math/birthday.htm (774 words)

	Parapoetica: Birthday Paradox (Site not responding. Last check: 2007-11-07)
		I’m a pretty skeptical guy; I don’t believe in homeopathy, astrology, or premonitions, and I read James Randi on a regular basis (though his vitriol impedes his ability to convince the faithful).
		Here’s the paradox: In a group of 23 people, there’s a 50% chance that two will share the same birthday.
		Well, the odds of Carol dreaming about Donna (of all the people she could have dreamed of), and of Donna then choosing to look up Carol (of all her other old college friends) on that day (of all other days to start reminiscing) are quite low.
	www.jay.fm /blog/birthday-paradox.html (443 words)

	Birthday paradox - All About All (Site not responding. Last check: 2007-11-07)
		For a greater than 50:50 chance that one person in a roomful of n people has the same birthday as you, n would need to be at least 253.
		For variations of the birthday scenario in broader contexts, a different flavor of argument is essential.
		In his autobiography, Halmos deplored the fact that the birthday paradox is often presented in terms of numerical computation rather than more abstract concepts.
	www.answers-zone.com /article/Birthday_paradox (1425 words)

	Cryptology and the Birthday Paradox An Application of Mathematical Groups to Structures of Human Groups
		The birthday paradox is well known and appears in many popular books on mathematics.
		In the form in which it is most commonly stated, it says that if 23 (or more) randomly chosen guests attend a party, then the probability of two of them sharing the same birthday is greater than 50%.
		This is considered “paradoxical,” presumably because most people would guess that the probability is much lower (or, equivalently, would suspect that many more guests would be required for a 50-50 chance of having a pair of matching birthdays).
	www.comap.com /product?idx=705 (105 words)

	CS199 Birthday Paradox (lab)
		The Birthday Paradox is a classic of counting and probability, because it's so darn surprising.
		It's a paradox not because it's logically contradictory, but because the true answer is so different from the "intuitive" answer.
		Each time you click the "find-birthday" button, each turtle chooses a birthday and if any match, they are marked in red (three way matches in yellow and so forth).
	cs.wellesley.edu /~cs199/lectures/09-birthday.html (1463 words)

	The Birthday Paradox
		The answer to the birthday paradox is well known, but it's fun to derive it.
		The odds are calculated by counting all the ways that N people won't share a birthday and dividing by the number of possible birthdays they could have.
		If persons A and B don't share a birthday and B and C don't either, then the chance that A and C share a birthday is affected by that information.
	www.teamten.com /lawrence/puzzles/birthday_paradox.html (910 words)

	WFMU's Beware of the Blog: The Birthday Paradox
		To celebrate Sluggo’s birthday, I took time off from my dayjob and we went to see the Egon Schiele show at the Neue Galerie.
		That thing about 2 out of 23 people in a room sharing the same birthday is known as the Birthday Paradox, but I think the real paradox is that every birthday brings you closer to the end of having birthdays.
		I was looking at all the people who showed up for Listener Smartski’s birthday party the other night and wondering how many people would show up for my birthday party, if I ever had one, and then I got to wondering how many people, if any, would show up for my funeral.
	blog.wfmu.org /freeform/2006/02/the_birthday_pa.html (979 words)

	ipedia.com: Birthday paradox Article (Site not responding. Last check: 2007-11-07)
		2 A mathematical, as opposed to numerical, view of the birthday paradox
		To compute the approximate probability that in a room of n people, at least two have the same birthday, we disregard leap years and twins, and assume that the 365 possible birthdays are equally likely.
		A mathematical, as opposed to numerical, view of the birthday paradox
	www.ipedia.com /birthday_paradox.html (789 words)

	Birthday - Birthday paradox - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-07)
		The person whose birthday it is will make a silent wish and then blow out A birthday is considered a special day for the person, and so the person will
		Describes the origin of birthday celebrations and various family and cultural traditions.
		The birthday paradox states that if there are 23 people in a room then there The key to understanding the birthday paradox is to realize that there are
	surffine.com /srfn/birthday.htm (253 words)

	Review
		In class, we were computing the probability of a birthday collision for a group of 30 people.
		Consider the following experiment: Extract one person from the population and insert in the group.
		would have different birthdays (the second would have to be different from the first AND the third from the other two).
	www.cs.fsu.edu /~breno/CIS-5357/lecture_slides/numbers/node1.html (122 words)

	Blog, Jvstin Style: The Monty Haul and the Birthday Paradox Problems
		The "Birthday Paradox" is in a similar vein, too.
		With 365 days in a year, you'd think it would have to be a lot...but thanks to the laws of permutations, you're at better-than-even odds at only 23 people.
		but look at it this way...given the first person, the odds of the second person not having the same birthday is (365-1)/365 (since it could be any other day of the year but the original person).
	www.skyseastone.net /jvstin/unjvst/003064.html (559 words)

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