Opposing events: One and only one of events A and B must occur. There is no third possibility except that A is B.
Mutually exclusive events? The intersection of events A and B is empty, and A and B are mutually exclusive events, also called incompatible events. ?
Mutex: For event A, B, A crosses B= empty set. That is, a and b can't happen at the same time. ? Mutually exclusive events only asked that two events should not happen at the same time. ?
One of the opposing events must happen. The two mutually exclusive events are called opposing events.
Opposition: a special case of mutual exclusion. In the case of mutual exclusion, it is also necessary to satisfy that A and B are complete sets. That is, A and B only appear once and must appear once. ?
The opposite event is that if one of the two events does not occur, the other event must occur, that is, the two times are mutually exclusive and form a complete set.
The specific difference between the two:
(1) for different angles. The former is aimed at whether it can happen at the same time, that is, two mutually exclusive events means it can't happen at the same time; The latter is aimed at whether there is influence, that is, two independent events mean that one event has no influence on the probability of the other event (note: not one event has no influence on the other event).
(2) The number of tests is different. The former is different events in one experiment, and the latter is different events in two or more different experiments.
(3) The probability formula is different. If A and B are mutually exclusive events, there is a probability addition formula P (A+B) = P (A)+P (B); If A and B are not mutually exclusive events, there is a formula P (A+B) = P (A)+P (B)-P (AB); If A and B are independent events, there is a probability multiplication formula P(AB)=P(A)P(B).
Must mutually exclusive events be an antagonistic event?
Opposition must be mutually exclusive, and mutual exclusion is not necessarily opposite.
For example, there are three balls of red, yellow and blue, and one person can only choose one. The three events of choosing red, yellow and blue are mutually exclusive and will not happen at the same time, but they are not antagonistic. Because you can choose blue or yellow instead of red. When there are only two balls, red and yellow, and one person chooses, if only one ball can be selected, the two events of choosing red and choosing blue are opposite. Because it is either red or blue.