P(A | B)= P(A∩B)/P(B)； P(A | B)= P(B | A)； 0≤P(B | A)≤ 1； P(A | B)= 1 If A and B are always true; P(A | B)= 0 if a and b are always false; P(A|B)=P(A) If b is always true; P(A|B)=P(B) If a is always true.
Extended data:
1, Overview of Conditional Probability
Conditional probability refers to the occurrence probability of event A under the condition that another event B has already occurred. Conditional probability is expressed as: P(A|B), which is read as "the probability of a under the condition of b". Conditional probability can be calculated by decision tree. The fallacy of conditional probability is to assume that P(A|B) is roughly equal to P(B|A).
Mathematician John Allen alan paul pointed out in his book Mathematical Blindness that doctors, lawyers and other well-educated non-statisticians often make such mistakes. This error can be avoided by describing the data with real numbers instead of probability.
2. Difficulties in conditional probability
Conditional probability is a necessary content in the senior high school mathematics college entrance examination. It is not only the difficulty of learning, but also the key to the three basic formulas of probability. Probability multiplication formula, total probability formula and Bayesian formula are all based on conditional probability, and the independence of events is also defined by conditional probability. How to break through the difficulty of conditional probability and win the college entrance examination has become a difficult problem for many students.
First of all, the definition (concept) of conditional probability is difficult to understand; Secondly, it is difficult to calculate conditional probability, especially when using conditional probability in comprehensive probability problems.
3. The reason why conditional probability is difficult to grasp.
First of all, the concept of conditional probability is not well understood. Secondly, the calculation of conditional probability fails to grasp some common models, which can also be summarized as insufficient summary. Thirdly, when encountering the probability application problem, we failed to grasp the essence of the problem and quickly established the mathematical model, that is, the probability model, and the mathematical modeling ability was not strong. In a word, the problem of conditional probability is due to unclear concept, unclear nature and weak modeling ability.
4. Five common calculation methods of conditional probability
There are generally five methods for conditional probability calculation: one is to convert it into unconditional probability calculation; The second is the simple counting method of classical probability class; The third is to define the calculation method; The fourth is the calculation method of natural law; The fifth is the calculation method in statistical data.