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Kamis, 14 Juli 2011

Why study mathematics-probability and the birthday paradox

Main University mathematics decided to be, in order to complete this degree, the two required courses-advanced calculus-et probability theory and mathematical statistics is 52. Even though I was hoping the probability, number, and tend to be within a game of chance given course quickly this theoretical math course was no walk in the Park. Despite this, the birthday paradox and the math behind it [NULL] learned about in this process. Yes, twenty-five people in the room at least two common birthday probability to share more than 50-50. Read on and see why.

Birthday paradox probability's most famous and well known is one of the problems. In a nutshell, this problem "room for about twenty-five people, should be at least a couple common birthday is the probability?" asks a question. Some of you intuitively to speak if you connect with people in your everyday life to experience the birthday paradox. For example, have you ever remember you just met at a party and someone talking casually as his brother, your sister was looking for such birthday? In fact, after reading this article on this phenomenon and mind when you start to form a birthday paradox is more common than you think on the fly.

Twenty-five people in a common birthday of room two people to be better than the odds of it seems improbable, because possible 365 birthdays can fall, even. And yet, if this completely. Memories. The key is that we do not say that any two people are just some of the common date would hand should be a common birthday. For more information about this fact appears on behind the scenes is a math test. The beauty of this description is the arithmetic for more than a basic understanding will not require you to be ( arithmetic magicsee) the importation of this paradox. That's right. Combination analysis, permutation theory, no not any of these complementary probability space-you do not need to be versed in! Need to do is to put your thinking cap with me came this quick ride. Let's go.

Birthday paradox to understand we must first issue a simplified version will see. Let's for example 3, the probability of the appearance and ask others they must be a common birthday. Supplement issues, several times the probability of problem is resolved. What does it mean we this is very simple. In this example, the issues that are given to the two of them to have a common birthday probability. Supplement No problem to have a common birthday probability. Their common birthday or not; These two possibilities and therefore, the approach we take to resolve the issue. This completely person A or B two situations are similar if they choose to, and then B, and Vice President on the other hand, did not choose.

Birthday problem three people A choice or probability have two common birthday. let's be Then select B, or both to have a common birthday probability. Probability problem, experimental probability sample results to make space. This sunny, 10 balls in the bag to take 1-10 of numbering. Probability space 10 numbered consists of a ball. The probability of the entire space is the same one, always, and some forms of any event space probability always some fraction less than or equal to one less. For example, numbered in the scenario that the ball out of the bag to the pool when he or she is any ball, the probability to choose the 10-10, or 1; However, certain numbered with the probability to choose the ball is 1/10. Carefully you'll notice the distinction.

Now only one ball number 1; Since I am 1/10 can be used to calculate the ball 1 numbering choices I want to know the probability or the probability that, as far as I can tell not a numbered ball minus the probability to choose one. Select not ball 9/10, since there is no other 9-ball and
1-9/10 = 1/10. In either case, I get the same answer. This is the same approach – albeit in a slightly different math-our birthday paradox to show the validity of the will take.

Three people, each one of this year's 365 days can be born in the observation (birthday problem for us to simplify the problem, ignoring leap years). Final answer for which you want to calculate the probability space, the denominator of the fraction, we get the first person born may, 365 days a year, the second person, third party observation. Therefore, the possibility of 365 products three times or 365 x 365 x 365. Now we at least have two common birthday, calculate the probability we calculate the probability that no two common birthday and subtract this from 1. Remember one A or B, and A = 1-B, A and B are two events represent the problem: in this case, the probability of A common birthday have at least two B two common birthday represents the probability that you have.

Now double-click the General birthday, we can picture a number of ways. Well the first person of the year was born in 365 days. The second order, not the first ones to match the birthday person then this person born in any of the remaining four days. Similarly, the third person with the first two and birthday in order to share, then this person must be born any remaining 363 days later we are 1 and 2 persons for 2, minus. Therefore, a common birthday to 3 the probability of no two people (365x364x363)/(365x365x365) = 0.992. Therefore, it is almost none of the specific group 3 other will share common birthday. Two or more common should be the probability is 1 birthdays-0.992 or 0.008. This means that there is a 1 to 100 shots two or more common birthday will be less than.

Now things we consider the size of a maximum of 25 people, quite a significant change. The same argument, such as in the case of math 3 people, we have a number by the total number of possible combinations of birthday room 25 x 365 twenty-five far 365x365x .... No two common birthday, you can share a number of ways to 365x364x363x the 341 x …. The quotient of these two numbers and 1-0.43 0.43 = 0.57. In other words, twenty-five people in the room at least two 50 50 chance will common birthday better than. Interesting, no? Some math amazing especially probability theory can be displayed.

Those whose birthday is today reading this article, or will be one soon, you too have a happy birthday. And your friends and family birthday songs gathered around the cake, I'm glad to be as fun as it will be another year-made to don't forget the birthday paradox. Isn't life Grand?

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