# Things are not so simple…

Annoying elevator
probability theory as a branch of mathematics, often in their daily lives. We generally make rough judgments about possibilities based on intuition or common sense. In most cases, this is very reliable. However, on many issues, the actual possibilities are far from people’s imagination, and some may even surprise people.
The physicist George Gabriel used to work in a seven-story building, often from his office on the second floor to an office on the sixth floor. It may be a bit strange that when he waited for the elevator, he hoped that the elevator was going up, but in fact the elevator almost always went from top to bottom. However, whenever he was going down the sixth floor, the elevator parked in front of him always went up.
In fact, the explanation for this phenomenon is very simple: if you are waiting for the elevator at the lower floor, most of the time the elevator is always above you, so when you stop at your floor, it goes down; on the contrary, if you are on the upper floor close to the top floor Wait for the elevator, then the elevator is often below you again, so it goes up when it stops in front of you. However, people often imagine intuitively that no matter which floor the elevator is on, the possibility of going up or down should be similar.
The problem birthday
one to calculate the probability of the most difficult problems, it is believed that mathematicians so-called “birthday problem.” Suppose you are attending a party where 23 people are present. How likely is it that two of them were born on the same day and the same month? Perhaps, intuitively, you will feel that this possibility is very small. In fact, among 23 people, there is basically the same possibility that there can be a pair of the same birthday and all these people have different birthdays.
The more people there are, the faster the likelihood of having the same birthday increases. If there are 30 people, this possibility is greater than seven in ten. If it is 50 people, the probability will be greater than 97%! Seeing this, maybe you will try it yourself when there are 23 or more people in the future.
Why do rumors spread like wildfire
There is another phenomenon that shocks the judges of intuitive probability, and that is the “small world problem.” This kind of thing is not uncommon: you meet a stranger from afar, and through conversation, you find that you have a friend you know in common. Perhaps one of you will scream in surprise: “This’world’ is too small!”
Indeed. Sociologists at the Massachusetts Institute of Technology found through research that in the United States, on average, everyone knows 500 people directly. Of course, everyone is a link in many different “acquaintance chains.” They further calculated that they randomly selected two Americans, such as Smith and Brown, and the probability of them meeting each other was only one in 200,000. However, if Smith knows someone, someone knows another person, and another person knows Brown, the probability is more than half.
The psychologist Stanley Milgram once studied the “small world problem.” He first identified a “target”-Alice, the wife of a young man who was studying to be a pastor in Cambridge, Massachusetts. Then, in Vichito, Kansas, I randomly found a group of people as “starters”, gave each of them a document, and asked them to send them an acquaintance who was most likely to know the “target”. The acquaintances who received the document will send it to their acquaintances in the same way, so that this “chain” will hopefully continue until it connects to the “target”. To Milgram’s surprise, only 4 days later, a man gave the document to the “target” and said, “Alice, this is for you.”
In this experiment, each The number of “intermediaries” in the “chain” is the least two, the most is 10, and the average is 5. However, if you ask someone to estimate in advance, most people guess that 100 is needed. It is not difficult to imagine that such an “acquaintance network” can explain why some rumors and interesting new jokes spread so quickly across the country.