(2) Impossible events: events that will not happen under condition S are called impossible events relative to condition S;
(3) Deterministic events: inevitable events and impossible events are collectively referred to as deterministic events relative to condition S;
(4) Random events: events that may or may not occur under condition S are called random events relative to condition S;
(5) Frequency and frequency: repeat the test for n times under the same condition S, and observe whether there is an event A, and call the frequency nA of the event A in the n tests as the frequency of the event A; Call the occurrence ratio of event A the occurrence probability of event A: for a given random event A, if the occurrence frequency fn(A) of event A is stable at a certain constant with the increase of test times, write this constant as P(A) and call it the probability of event A. ..
(6) Difference and connection between frequency and probability: The frequency of a random event refers to the ratio of the number of times nA of the event to the total number of times n of testing, which has certain stability and always swings around a certain constant, and with the increase of testing times, the swing amplitude becomes smaller and smaller. We call this constant the probability of random events, which quantitatively reflects the probability of random events. Frequency can be approximated as the probability of the event under the premise of a large number of repeated experiments.
1, basic concept:
The inclusion, union, intersection and equality of (1) events.
(2) If A∩B is an impossible event, that is, A ∩ B = Ф, then event A and event B are mutually exclusive;
(3) If A∩B is an impossible event and A∪B is an inevitable event, then event A and event B are mutually opposite events;
(4) When events A and B are mutually exclusive, the addition formula is satisfied: p (a ∪ b) = p (a)+p (b); If events A and B are opposite events, then A∪B is an inevitable event, so P(A∪B)= P(A)+ P(B)= 1, so there is P (A) = 1-P (B).
2, the basic nature of probability:
1) The probability of inevitable events is 1, and the probability of impossible events is 0, so 0 ≤ p (a) ≤1;
2) When events A and B are mutually exclusive, the addition formula is satisfied: p (a ∪ b) = p (a)+p (b);
3) If events A and B are opposite events, then A∪B is inevitable, so P(A∪B)= P(A)+ P(B)= 1, so there is P (A) =1-P (B);
4) The difference and connection between mutually exclusive events and opposing events, mutually exclusive events means that in an experiment, event A and event B will not happen at the same time, including three different situations:
(1) Event A occurs, but Event B does not;
(2) Event A does not occur, but Event B does;
(3) Event A and Event B do not occur at the same time, and the opposite event means that there is only one event A and Event B, including two situations:
(1) Event A occurs, but event B does not;
(2) Event B happens and Event A doesn't, which is a special case of mutually exclusive events.