Applicable scope of the lottery principle

When the sample population and the size of the sample drawn are not large, the lottery method is usually used.

The lottery method, the population is limited and easy to number. First number all the individuals in the population (the numbers can be from 1 to N), and write the numbers on the number tags of the same shape and size. The number tags can be used Make small balls, cards, paper strips, etc., then put these numbers in the same box and mix them evenly.

When drawing lots, one number is drawn from it each time, and a sample with a capacity of When drawing samples, students’ student numbers, seat numbers, etc. can be used. The lottery method is simple and easy to implement, and it is suitable to use this method when the overall number of individuals is small.

Principle of drawing lots

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. There are 4 difficult lots among the 10 test lots. 3 people participated in the lottery (no replacement), A first, B second, and C last. Please ask A to draw the difficult lot. A and B both drew the difficult lot, but A did not draw. The probability of a difficult draw and that B draws a difficult draw and that A, B, and C all draw a difficult draw.

In fact, even if these ten lots are drawn by 10 people, because there are 4 difficult lots among them, the probability of each person drawing a difficult lot is 4/10, regardless of the order in which he draws. .

Just like if there are only 10 grand prizes out of 100,000 lottery tickets, they will be drawn by 100,000 people. Regardless of the order, everyone's probability of winning is 10/100,000, that is, 1/10,000. This is called the principle of drawing lots in probability theory.

This type of question often appears in graduate entrance examination questions. If you know it, you can answer it quickly, otherwise you may make a mistake. In the oral test of drawing lots, there are a+b different test tickets. Each candidate draws 1 test ticket. The drawn test tickets will not be put back. A certain candidate will only take a test among them, and he is the kth one. For drawing lots, find the probability that the candidate will draw a lot for the general examination.