Binomial distribution is generally used for independent repeated experiments, and its characteristic is "what is the probability of n times"; Hypergeometric distribution usually asks "What is the probability of the nth appearance?"

It should be that binomial distribution model cannot be used, and it is not an independent repeated experiment unless it is put back.

In a word, one is extraction with replacement (binomial distribution) and the other is extraction without replacement (hypergeometric distribution).

For example, there are 5 black balls and 15 white balls out of 20 balls. If you draw three times and put it back each time, the probability of drawing a black ball each time is 1/4, which is independent of other times. This is obviously an independent repeated experiment, and the corresponding probability model is binomial distribution.

The characteristics are still obvious. For example, I took the above example six times. If I don't put it back, there are at most five black balls in it. But if you put it back and draw it, you can draw all six black balls.

There is also a connection between the two, that is, when the total number is very large compared with the number of draws, the two are very close. For example, 65,438+0,000 balls, of which 200 are black and 800 are white, are drawn three times. If the probability of drawing a black ball at a time is 1/5, then the probability of drawing it for the first time without putting it back is 1/5. The second time, if the first time for white is 200/999 or about 1/5, the first time for black is 199/999 or about 1/5, and so is the third time. The probability of each time is about 1/5, which can be distributed according to binomial.

Binomial distribution is used in n independent repeated experiments. For example, if the probability of coin flip is 0.5, the probability of coin flip 10 and three heads-up events can be regarded as three heads-up events in 10 independent repeated experiments. Binomial distribution.

The model of hypergeometric distribution is: there are 100 products, including 3 defective products, and 5 products are extracted at a time. The probability of extracting the number of defective products is hypergeometric distribution.

Usually, the classical probability is a discrete random variable.

For example, the experiment of throwing a dice with uniform texture. What are the possible results of classical probability in these two experiments?

For the probability problem in senior high school, we should do more examples, summarize them and analyze the specific problems. It's hard to say whether this model is absolutely useful or not.