two events
Definition: Suppose A and B are two events. If is satisfied, then these two events are called Mutual independent.
If, then A and B cannot be independent and incompatible with each other at the same time.
Mutually independent means that the occurrence of one event has no relationship with whether another event occurs. Mutually incompatible means that two events cannot occur at the same time.
Example 1:Tourist A went to Beijing this afternoon, and tourist B went to Beijing this afternoon. These two events are independent of each other (assuming they did not make an appointment to go together) .
Example 2:Tourist A went to Beijing at 14:00 this afternoon, and tourist A went to Shenzhen at 14:00 this afternoon. These two events are incompatible with each other.
- Suppose A and B are two independent events, and
, then
,
- Suppose A and B are two independent events,
is the inverse event of A,
is the inverse event of B, then A and
Three events
Suppose A, B, and C are three events. If the probabilities satisfy the following relationship:
Then these three events are said to be independent of each other.
Multiple event situations
For events, among which
, if any 2, 3,..., the probability of any n product events, are equal to the product of the probabilities of their individual events, then these n events are said to be independent of each other.