Assessing Students’ Difficulties With Conditional Probability

With the development of probability theory, corresponding education has been added to our country’s high school mathematics subject. We could find the contents of condition probability from the textbook of Prentice Hall and Panpac Education, which proves that the study of condition probability is valuable. This paper aims to make a deep contrast of comprehensions between students who have studied condition probability and students who have not in order to make an improvement of education service.This paper considers the difficulties when solving conditional probability of students who study liberal arts and has not learnt conditional probability, students who study science and has not learnt conditional probability, students who study science and has learnt conditional probability based on a combination of survey and interview. Major issues this paper has investigated are as follows:1、What kind of errors would students make when solving conditional probability?2、re there differences in solving the problems and figuring out their errors among the three kinds of students mentioned above?3、What are the attitudes of teachers in teaching conditional probability?Based on a survey of255students and interviews of12students and2teachers, this paper finds that the students’errors of conditional probability could be considered in these three aspects:what is condition, how to utilize condition, and how to use classic probability. As to what is condition, we could find three problems, those are,"causal bias"、"fallacy of the time axis" etc; as to how to utilize condition, three problems are also be detected, those are,"P(A|B)=P(AB)" etc; when it comes to how to use classic probability, the major problem is "fallacy of sample space". From all these ones,"not sensitive to the text description of the conditions"、"P(A|B)=P(AB)"、"fallacy of sample space" are most frequently happened. The three kind students behave apparently different when they are dealing with the three major problems, which indicate that these three major problems could be prevented by suitable education. However, we could not see any distinct differences from behaviors of all students as to the problems of "causal bias" and "allacy of the time axis", which reveal that those problems could be inflexible. This paper also finds that our teachers have not paid enough attention to the education of conditional probability which holds only a few shares of the final test.