Conditional probability is the probability of occurrence of A under the premise of occurrence of B. When setting events, you should set the probabilities of occurrence of A and B as P (a) and P (b) respectively, and then see what you can calculate according to the meaning of the question.

Example:

Have a classmate, the probability of failing math is 0. 15, the probability of failing Chinese is 0.05, and the probability of failing both is 0.03. In an exam, it is known that he failed in math, so what is the probability of his failing in Chinese?

Note that event A is "failing math" and event B is "failing Chinese", so P(A)=0. 15 P(B)=0.05, P(AB).

=0.03, then p (b ~ a) = p (ab)/p (a) = 0.2.

Extended data:

probability measure

Probability p (b) if event b >; 0, then the function q defined by Q(A) = P(A | B) on all events a is a probability measure. If P(B) = 0, then P(A | B) is undefined. Conditional probability can be calculated by decision tree.

Joint probability

Represents the probability that two events will happen together. The joint probability of a and b is expressed as P(AB) or P(A, b) or P(A∩B).

marginal probability

Is the probability of an event, which has nothing to do with other events. The marginal probability is obtained as follows: in the joint probability, those events that are not needed in the final result are merged into the total probability of their events and disappear (for discrete random variables, the total probability is obtained by summation, and for continuous random variables, the total probability is obtained by integration).

This is called marginalization. The marginal probability of a is marked as P(A), and the marginal probability of b is marked as P(B).

Reference: Baidu Encyclopedia-Conditional Probability