Candidates who take the civil service exam often ask such a question: "I don't want to draw the first sign in the interview lottery, I will be nervous, and I hope to draw the sign in the lower order." Which one should I draw to take advantage? " In fact, there are advantages and disadvantages in drawing lots, so don't worry. Chinese public education experts discuss the mathematical thought behind this with candidates today.
For example, the Chinese zodiac sign up for the civil servants in Tiangong together, and as a result, everyone tied for the first place, so the final candidate was decided by drawing lots. There is only one quota, and the mouse is the first to draw lots, so the probability of winning the prize with the mouse is112, which is easy to understand. What are the chances that the cow will win if he comes second? Many students will make mistakes here. They thought that a * * * hit a lot, the mouse smoked one, and there were eleven left. So the probability of winning the lottery should be111. In fact, students who understand it this way ignore a condition, that is, if a cow wants to win, it must be a mouse, so the probability of a cow winning should be that the first mouse doesn't win multiplied by the second cow wins, that is,112×11/. Similarly, when the tiger draws the third time, the winning probability is that the mouse fails to draw for the first time, multiplied by the cow's failure for the second time, and then multiplied by the tiger's failure for the third time, that is,112×11× By analogy, the winning probability is112 in any lottery. Therefore, drawing lots is an absolutely fair game. No matter which draw you are, the probability of winning is the same.
Of course, the above examples are only compiled by Chinese public education experts, and civil servants cannot have such doubts. So let's look at such a question:
A bag contains 10 balls, including 4 white balls and 6 black balls. If you draw one at a time and don't put it back, what is the probability of drawing a white ball for the second time?
If this problem is a conventional solution, it should be discussed in categories. Suppose the first one is a white ball, and the probability is1; Suppose the first one draws a black ball, we get a probability of 2, and the sum of probability 1 and probability 2 is the answer we are looking for. This solution takes a lot of time. If you ask the probability of winning the third or even the fourth white ball, the workload will double.
Chinese public education experts also want to tell candidates that if we use the concept that lottery is an absolutely fair game, we will know that no matter which lottery, the probability of winning the white ball is the same as that of the first lottery, which is 4/ 10, and the problem can be solved quickly.
If in doubt, please consult the public education enterprises in China.