3) Conditional probability: Considering the probability of event B when event A has already occurred.
Definition: Let A and B be two events, P (a) >; 0, indicating
P(B|A)=P(A*B)/P(A) .................... formula 3
Is the probability that event B will happen if event A has already happened.
Understanding: it is P (intersection of A and B) /P (set A)
Understand:? What is the probability that event B will happen when event A has already happened? Obviously, when saying this sentence, both A and B happened, and we require the ratio of A and B happening at the same time to A, that is, the probability ratio of A and B happening at the same time to A. ..
Total probability theorem
The occurrence of event A always occurs under some other conditions, such as B, C and D, which means that the probability of A is actually the sum of the probabilities of A under the conditions of B, C and D. A has conditional probability when B occurs, C occurs and D occurs. If b, c and d contain all the conditions of a, then, a?
P(A)=P(A|B)+P(A|C)+P(A|D)
4) Independent events and probabilities
The two events are independent, that is to say, whether A and B occur or not does not affect each other. A is a, b is b, expressed by the formula P(A|B)=P(A), then the probability of two things happening at the same time is:
P(A U B)=P(A)? P(B) ................ formula 4
I hope that the above common conclusions about conditions and the probability of independent events will be helpful to everyone, and it is very useful to keep these knowledge in mind. I wish you all success in the GRE exam!