In probability theory, the horizontal line above a represents the inverse event of an event. This situation is silent, so it is directly called the inverse event of A, also called the inverse event of A. ..

definition

If A and B are impossible events and A and B are inevitable events, then A and B are mutually opposite events, that is to say, A and B must occur and only one event can occur.

Probability relation of opposing events: P(A)+P(B)= 1. For example, in the dice test, A={ the number of points appearing is even}, b={ the number of points appearing is odd}, A∩B is an impossible event, and A∪B is an inevitable event, so a and b are opposite events.

Extended data:

Exclusive activity

If event A and event B cannot occur at the same time, then event A and event B are mutually incompatible events, and mutually incompatible events are also called mutually exclusive events. It means that event A and event B will not happen at the same time in any experiment.

Mutual exclusion and opposition of opposites

The connection between mutually exclusive events and the opposite event is that the opposite event belongs to a special mutually exclusive events.

The difference between the two can be seen through the definition: the union of an event itself and its opposite events is equal to the total sample space; But if two events are mutually exclusive events, it means that one event will not happen, but it does not emphasize that their union is the whole sample space. That is, opposites must be mutually exclusive, and mutual exclusion is not necessarily opposite.

The difference between mutually exclusive events and independence events is roughly as follows:

1, for different angles. The former is aimed at whether it can happen at the same time, that is, two mutually exclusive events means that it is impossible for the two to 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.

Note: Not one event has no effect on another.

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).