Catch the ball and draw lots.
So the probability of the tenth person getting the yellow ball is the same as that of the first person, which is 2/5.
Let me give you a simple example. Suppose there are two red balls and one Huang San ball. If three people take the ball and don't put it back, what is the probability that the third person will get the yellow ball?
The probability of the first person getting the yellow ball is 1/3, the probability of the second person getting the yellow ball is (2/3)*( 1/2)= 1/3, and the probability of the third person getting the yellow ball is (1/3) */kloc-
It can be seen that the order of drawing lots is irrelevant.
The principle of lottery comes from the formula of total probability.
It means that the lottery order has nothing to do with the probability of winning.
For example:
10 trial draw, 4 difficult draws, 3 people participating in the draw (not put back), A first, B second, C finally, A draws the probability of difficult draws, A and B both draw difficult draws, A does not draw difficult draws, B draws difficult draws, A, B and C all draw difficult draws.
In fact, even if these ten tickets are drawn by 10 people, because four of them are difficult to draw, the probability of each person winning the ticket is 4/ 10 regardless of the order in which he draws.
Just like 100000 people draw 100000 lottery tickets with only10 grand prize, in no particular order, everyone's winning probability is10000010, which is one in ten thousand.
This is called the lottery principle in probability theory.
This kind of problem often appears in the postgraduate entrance examination questions. Answer as soon as you know, or you may make mistakes.
In the oral test of the lottery, * * * has a+b different test pieces, and each candidate takes 1 test piece, which will not be put back. A candidate will only take one of them, and he is the k lottery. Find the probability of candidates taking samples in HKCEE.
Analysis: Because everyone draws a test paper at random, the result obtained by each person after drawing lots is equivalent to a complete arrangement of these test papers, and the possibility of different arrangement results is the same. This question is about the probability of waiting for possible events. Because it is the first time for candidates to draw lots, they can draw a test paper in HKCEE, which is one of the A papers of someone's HKCEE. We can use the knowledge of permutation and combination to find out all the different numbers of this permutation.
Solution: this question is the probability problem of equal possible events. The total number of all different lottery results for A+B candidates.
Because,
When a candidate draws the lottery for the k th time, he just draws one of the A test labels in HKCEE, which is equivalent to that the K test label in all lottery results is 1 in the A test label. The total number of all the lottery results we can get is:
Therefore, the probability of a candidate getting a test paper is:.
Note: Judging from the calculation results, the number of lucky draws has no influence on the candidate's probability of winning HKCEE, that is to say, no matter what number of lucky draws he takes, it will not affect his possibility of winning HKCEE. There is such a problem in daily life: 10 has a winning lottery ticket, and now 1 0 people want to touch the lottery ticket, first modeling and then touching the winning one. Now we can calculate the result of this problem. Now suppose you are the m-th person to win the prize. In order to calculate the winning probability, first calculate 10. All possible results of winning the prize are 10! And the winning lottery ticket happens to appear in the m th place. All possible outcomes are 9! In this way, it can be concluded that the probability of winning the lottery is 0, and the result has nothing to do with M, so don't worry about being won by others.
Suppose that only one person wins the prize, because the second winning prize is based on the first not winning the prize, so the first step is to calculate the probability of the first not winning the prize, and then multiply the probability of the second winning prize according to the multiplication principle. So you see that * * * is five lots, one lot is a prize, and the other four lots are not. The first person chose one among those who didn't win the prize, so it was A4 1. The second person won the prize, representing A 1 1. The basic event is to draw two A52 out of five, so it is A4 1 1/A52, that is, A4 1/A52. You can read the math textbook for the second grade.
In fact, it can be understood as follows: the probability of the first person not winning is 4/5, and the probability of the second person winning is 1/4, so it is 4/5* 1/4.