The same day, how many have the edge?

The same day, how many have the edge?

Beijing News weekly of the new knowledge

Everyone has a birthday, an occasional encounter with his birthday on the same day, but in life, this fate did not seem to have.

We guess, in the 50 's, the probability of fate, is 10%, 20% or 50%?

I have been told that in the article Insert a formula very turnoff, do not write the calculation process (in addition to the traditional method of permutations and combinations, the United States mathematician Paul ·

Har Moss also gives a clever solution to), directly to the result. In 50 people have the same birthday of probability, as high as 97% of this figure, fear that go far beyond most people expected.

Believe me, wrong not the calculation process, but intuition.

In this place, science and daily experience with us a joke. Because of calculation results and daily experience the apparent contradiction, the problem is referred to as "the birthday paradox" (BirthdayParadox). It manifests is rational calculation and sensibilities of contradictions, and does not cause logical contradictions, so it is not in the strict sense of the paradox. "Birthday paradox" of the original expression is: 23 individuals who has the same birthday of probability greater than 50%. In order to highlight the contradictions, I've come to the number 50. If you don't know the answer, judging, you guess the result certainly far less than 97%? here, maybe someone will ask our calculations, it is assumed that people's birthday uniform random distribution, but life is not necessarily the case — don't worry, mathematicians have long considered this factor, is not evenly spread situation has been resolved, but further proof that the uneven distribution, the probability is only higher. In addition, the United States computer scientists Gartner (d.e.knuth) also calculated the question: how many people in average in order to find an answer to the same birthday? is 25 persons. This looks really weird?

For why this contradiction? in fact the problem is not complicated.

First, when only one individual, the "same birthday" probability is 0%. If you do not take into account leap years and the number of factors, when greater than 365, "the same birthday," the probability is 100%. Thus, in the range 1 to 365 within this interval, we typically will naturally believe that corresponds to the probability is linearly with increasing from 0% to 100%, even if it is not linear, it will not be too excessive, steep for 50 people, the probability should be 50/365, or 13.7%. But in fact, this curve of growth momentum is terrible: from skyrocketing, and 50 people, the chance has been close to 100%, and we have a linear curve of fantasy. So the question is: why we will assume that it is linear? don't worry, we put a little alteration, to get inspired. The new issue is, in a group of people among them, someone with you on the same day, birthday, this probability? Similarly, we put the probability curve drawing it out, you can see, it is a very gentle: number of 350, this probability but slightly higher than 50%. (Below figure)

Now, we can generally be found above the error causes of intuition: when we see the same "someone's birthday," subconscious "and my birthday is the same as the" go to speculate that the rocket for a steady growth, resulting in a "birthday paradox".

□ Su coconut (Jiangsu artificial intelligence professional)