Firstly, all possible values of the random variable zeta are determined, and then the probability of each value obtained by zeta is calculated;

All the probabilities can add up to 1. Check whether the calculation is correct.

Then make a list and draw a distribution list;

Finally, according to the requirements of the topic, seek mathematical expectations or other questions.

As for the method of obtaining each probability value, it can be obtained according to different types of questions; The simpler the classical probability; There are also binomial distribution tables and hypergeometric distribution tables, which can be found by formulas; Then there are some special distribution lists, which are analyzed according to the meaning of the question.