生活中对概率的错误感觉

生活中对概率的错误感觉
一、
轮盘游戏：在游戏中玩家普遍认为，在连续出现多次红色后，出现黑色的机率会越来越大。

这种判断也是错误的，即出现黑色的机率每次是相等的，因为球本身并没有“记忆”，它不会意识到以前都发生了什么，其机率始终是18/37。

（注：只有考虑综合情况时，可以按照条件重新计算。

）
二、
2. 生日悖论：在一个足球场上有23个人（2×11个运动员和1个裁判员），不可思议的是，在这23人当中至少有两个人的生日是在同一天的机率要大于50％。

所以所有人生日都不相同的概率是：
(365/365)×(364/365) ×(363/365) ×(362/365)×... ×【(365-n+1）/365】
那么，n个人中有至少两个人生日相同的概率就是：
1-(365/365)×(364/365) ×(363/365) ×(362/365)×... ×【(365-n+1）/365】（注：可写为１－ｐ（３６５，ｎ））
所以当n=23的时候，概率为0.507
当n=100的时候，概率为0.9999996
三、
三门问题
在电视台举办的猜隐藏在门后面的汽车的游戏节目中，在参赛者的对面有三扇关闭的门，其中只有一扇门的后面有一辆汽车，其它两扇门后是山羊。

游戏规则是，参赛者先选择一扇他认为其后面有汽车的门，但是这扇门仍保持关闭状态，紧接著主持人打开没有被参赛者选择的另外两扇门中后面有山羊的一扇门，这时主持人问参赛者，要不要改变主意，选择另一扇门，以使得赢得汽车的机率更大一些？正确结果是，如果此时参赛者改变主意而选择另一扇关闭著的门，他赢得汽车的机率会增加一倍。

Now I will tell you some examples and problems that we may have a illusion of probability in our life.
1 one, roulette game(it is just a game that we play with a turntable----spinning disk with numbers on different parts of it)In this game, gamblers generally believed that when the same numbers appears many times in a row, the probability of appearing that number will decrease. Actually, the judge is wrong. The truth is, every time there is equal probability of each number, because the turntable itself does not have "memory", it can not realize what has happened before, the probability will be always the same.
2. Birthday paradox: (it is called a paradox because it is different
from most people’s opinion)
on a soccer field(imaginary), 23 people (2 ×11 players and a referee). It is incredible that in these 23 people, the probability of there are two people was born on the same day is greater than 50%.
First, we can get the probability of everyone was born on a different day is: (365/365) ×(364/365) ×(363/365) ×(362/365) ×... ×【(365-n +1) / 365】
Therefore, the probability of there are at least two people with the same birthday is: 1 - (365/365) ×(364/365) ×(363/365) ×(362/365) ×... ×【(365-n +1) / 365】
So, when n = 23, when the probability of 0.507 when n = 100 when the probability of 0.9999996
3.Monty Hall Problem
Came from a game show held in the television. The rule of this game is easy, there are three doors in the room, a bag of treasure was hidden behind one of the door. Behind other doors are a goat. The participants of the game will stand opposite three closed doors, of which only one has treasure behind it. First, participants select one door, but the door will still be closed. Then the host of this show will open another door with a goat in it, when the host asked the participant if he wants to change his mind.
So, will the participant has a greater probability to win the car?
We can use enumeration to sovle this problem.
Or we can think of it in this way: suppose we want to change the door we have chosen before, then if we choose door A(with treasure) in the beginning, we won’t get the money. If we choose door B or door C in the beginning(without treasure), we will get the money at last. So if we choose to change our mind, we will have 2/3 probability to win.
The result is that if participants change their minds at this time to choose another door closed doors, he won the chance to double the car.。