Scope of application of the lottery principle

When the sample population and sample size are small, the lottery method is usually used.

The lottery method is limited in the whole population and easy to number. Firstly, all individuals in the whole population are numbered (the numbering range can be 1 to n), and the numbers are written on numbers with the same shape and size. Numbers can consist of balls, cards, paper strips, etc. Then put these numbers in the same box and mix them evenly.

When drawing lots, every time 1 number is drawn, a sample with a capacity of is obtained. When numbering individuals, you can also use the existing number, for example, when taking samples from the whole class, you can use the student's student number and seat number. The lottery method is simple and easy, and it is suitable for the situation that there are not many individuals in the whole population.

Draw lots principle

The principle of drawing lots comes from the total probability formula, which means that the order of drawing lots has nothing to do with the probability of winning lots. 10 test lottery, 4 difficult to sign, 3 people to participate in the lottery (not put back), A first, B second, C finally find the probability that A is difficult to sign, A and B are difficult to sign, A is difficult to sign, B is difficult to sign, A, B and C are difficult to sign.

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 decided by lot, there are a+b different samples, and each candidate takes 1 sample, and the extracted samples will not be put back. A candidate will only take one of them, and he is the k lottery. Ask candidates the probability of taking samples in HKCEE.