Probability theory and mathematical statistics are statistics on the phenomenon of the random one of Mathematical S Random phenomenon exists because of the universality, makes a lot of scientific research, engineering, economic, agricultural production and management of the area is also an increasing number of applications , For the modernization drive has made an important contribution to modern science and technology with the rapid development of mathematical subjects that the door has been vigorous development, and formed a large structure of the Since the actual probability and statistics and abstract, it's There are a lot of problems-cases, there is a need for statistical probability of counter-examples to the The text introduces the probability of random events and issues of counter-examples; discrete random variables related to the distribution and continuous random variable distribution of counter-examples; independence and related issues in the Phase capacitive on the counter-examples; number of characteristics of the random variable The counter-examples of; parameters estimates and assumptions in the anti-testing case of The text of each type of counter-examples of the problems described in detail and analysis, are given specific examples, and to compare and analyse them, then the probability and statistics With the issue of anti-profound understanding, and deepen the understanding of probability and statistics and Key words: random events; distribution function; counter-examples; joint distribution; probability estimates;