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"Interesting Mathematics" in Life

Mathematics often makes smart people feel stupid, and sometimes it even makes them angry. In fact, mathematics itself is very interesting. It is a part of our daily life and everyone can enjoy it. Only in class, math is taught by some rigid teachers. The following is an interesting math in daily life published in the British Daily Mail: The probability of having a birthday on the same day Suppose you are attending a wedding of 50 people, and someone asks, "I want to know, what is the probability that two people are here with the same Armano?" Perhaps most people think this probability is very small, and they may try to calculate it. I guess this probability may be 1/7. However, the correct answer is that only about two guests from the same family attended the wedding. If this group of people's birthdays are evenly distributed at any time of the year, then the probability that two people have the same birthday is 97%. In other words, you have to attend 30 parties of this size to find that none of the guests have the same date of birth. The probability that two specific people are born at the same time is 1/365. The key to answer this question is the size of the group. As the number of people increases, the probability that two people will be in the same Amanome will increase. In a group of 10 people, the probability of two people in the same Amanome is about 12%. In a gathering of 50 people, the probability is about 97%. However, only when the number rises to 366 (one of whom may have been born on February 29th) can you be sure that the two people in this group must be the same Amanome. How many socks can I take to make a pair? The answer to the question how many pairs of socks can be paired is not two. I can guarantee that if I take out two socks from the drawer on a dark winter morning, they will definitely not match. But if I take out three socks from the drawer, I will definitely have a pair of socks of the same color. Whether the socks are black or blue, there will be a pair of the same color in the end. Of course, this is only true if the socks are two colors. If there are blue, black and white socks in the drawer, you must take out at least four pairs if you want to take out a pair of socks with the same color. If there are 10 pairs of socks with different colors in the drawer, you must take out 1 1 pairs of socks. According to the above situation, the mathematical rule is: if you have n kinds of socks, you must take out N+ 1 to ensure that one pair is exactly the same. It takes 1 hour to burn a rope from one end. Now you need to use this rope and a box of matches to measure for half an hour without looking at your watch. You may think it's easy. You just need to make a mark in the middle of the rope, and then measure the time it takes for the rope to burn halfway. Unfortunately, however, this rope is not uniform. Some places are thick and some places are thin, so this rope burns at different speeds in different places. It may take only 5 minutes for half of the rope to burn, and 55 minutes for the other half to burn. Faced with this situation, it seems impossible to accurately calculate the time of 30 minutes by using the rope above, but this is not the case. You can solve the above problems in an innovative way. This method is lit from both ends of the rope at the same time. The rope must take 30 minutes to burn out. The problem of trains running in opposite directions Two trains are running in opposite directions along the same track, and each train runs at a speed of 50 miles per hour. When the distance between two carriages is 100 mile, a fly flies from train A to train B at the speed of 60 miles per hour. When it meets the train B, it immediately turns around and flies to the train A, and so on until the two trains collide and crush the fly into pieces. How far did the fly fly before it was crushed to death? We know that the distance between two cars is 100 mile, and the speed of each train is 50 miles per hour. This means that each train travels 50 miles, that is, two cars collide one hour later. During the hour from the departure of the train to the collision, the fly kept flying at a speed of 60 miles per hour, so when the two cars collided, the fly flew 60 miles. Whether the fly flies in a straight line, along a "Z" line or rolls in the air, the result is the same. Flipping a coin is not the fairest. Flipping a coin is a common way to make a decision. People think this method is fair to both sides. Because they think that the probability of coins falling backwards is the same as that of coins falling backwards, both of which are 50%. Interestingly, this very popular idea is not correct. First of all, although it is unlikely that a coin will stand on the ground when it falls, this possibility exists. Secondly, even if this small possibility is ruled out, the test results show that if you flick the coin with your thumb in a conventional way, the probability that the coin will still be up when it hits the ground is about 5 1%. The reason why this happens is that with a flick of the thumb, sometimes the money will not turn over, but will only rise like a trembling flying saucer and then fall. If you want to choose next time, look at which side is up first, so you have a greater chance of guessing correctly. But if that person is holding coins and turning his fists one by one, then you should choose the opposite from the beginning. Author:) (This article Source: Yangcheng Evening News)