In the topic, there is little need to judge independence, or obvious independence, because the two events A and B do not interfere with each other. Most questions will say that A and B are known to be independent, that is, they will tell you in advance without judgment.
Another kind of topic is to judge independence by formulas. Generally, it is to tell you the distribution list of an independent random variable, find one of its parameters or ask whether it is independent.
Use the formula: P{X=i, Y=j}=P{X=i}*{Y=j}
Extended data of any event P(AB)=P(A)-P(A non-B) P(AB)=P(B)-P (non-AB)?
If A and B are independent of each other, P(AB)=P(A)P(B)
When P(A) >; 0 P(AB)=P(A)P(B|A)
When P(B)>0 P(AB)=P(B)P(A|B)
Sometimes the probability is 0, such as incompatible events, such as A B is two incompatible events, A occurs, and P(B)=0. For example, when throwing a coin, it is heads, and the probability of tails is 0.