Why not put the sample back? Why are the probabilities equal?

For example, if 20 people are sampled, the probability of each person in the first round is 1/20, and the probability of each person not being selected in the first round in the second round is 19/20, then the probability of being selected now is119, and the two products are equal to/kloc-0. The probability has not changed.

It is a method of extracting individuals one by one, and the individuals extracted each time are not put back into the population to participate in the next extraction. When the non-repeated sampling method is adopted, the number of units in the population decreases gradually during the sampling process, and the probability of each unit being drawn in the population is different in turn. Non-return sampling also refers to the sampling method of sampling the whole sample at the same time.

Extended data:

Hypergeometric experiments have the following characteristics.

(1) Randomly select n samples from a population containing n individuals in a non-repetitive manner, and each experiment (sampling) is not independent.

(2) In the total N, there are K successful students and n-k failed students.

(3) In the sample, there are X people selected from the successful class and n-x people selected from the failed class.

(4) Because the test (sampling) is not repeated, the success probability of each test is affected by the previous test result, so the success probability cannot be maintained.

Among them, (N-n)/(N- 1) is called finite population correction factor, which should be considered when non-repeated random sampling is adopted, so it is also called non-repeated sampling correction factor.

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