The concept of 1. event:

(1) event: The result of an experiment is called an event. Generally use capital letters a, b, c,? Express delivery.

(2) Inevitable events: events that will occur under certain conditions. (3) Impossible events: events that will definitely not happen under certain conditions (4) Determinant events: inevitable events and impossible events are collectively called deterministic events.

(5) Random events: events that may or may not occur under certain conditions. 2. Probability of random events:

(1) frequency and times: repeat the test for n times under the same conditions to see if there is an event A, which is called n times of test.

The frequency An of event A in the test is the frequency of event A, which is called the occurrence ratio n of event A..

n

Fan? (for event a)

Frequency of occurrence.

(2) Probability: Under the same conditions, when the same experiment is repeated a lot, the frequency of event A will swing around a constant, that is, the frequency of random event A is stable. We call this constant the probability of random events, and write it as) (AP.

3. The essence of probability: the probability of inevitable events is 1, the probability of impossible events is 0, and the probability of random events is 0.

0() 1PA, inevitable events and impossible events are regarded as two extreme cases of random events.

4. Significance of the sum of events: The notation of events A and B is A+B, which means that at least one of events A and B occurs. 5. mutually exclusive events: In a randomized trial, two events that cannot occur at the same time in the trial are called mutually exclusive events. When A and B are mutually exclusive events, event A+B consists of "A happens but B doesn't happen" and "B happens but A doesn't happen", so when A and B are mutually exclusive, the probability of event A+B satisfies the addition formula: P(A+B)=P(A)+P(B)(A and B are mutually exclusive). Usually, if the event =

12()()()nPAPAPA？ .

6. Opposing events: Event A and Event B must have a mutually exclusive events. A and b are opposite, that is, events A and B cannot happen at the same time, but one of them must happen. At this time, P (a+b) = P (a)+P (b) = 1, that is, P (a+a) = P (a)+.

When the probability P(A) of event A is difficult to calculate, sometimes it is easier to calculate the probability of its opposite event A, so there is p (a) = 1-p (a).

7. Event and set: From the point of view of set, two events A and B are mutually exclusive, which means that the intersection of the set formed by the results of two events A and B is an empty set. The set of the opposite result of event A is the complement of the set of the result of event A in the complete set U, that is, A∪A=U, A∪A =? The opposing event must be mutually exclusive events, but mutually exclusive events is not necessarily an opposing event.

(2) Typical case analysis:

Example 1. Throw a uniform coin up 10 times, of which just five times are () A. inevitable events B. random events C. impossible events D. uncertain.

Example 2. Take out any two balls from the pocket containing two red balls and two white balls, then two events that are mutually exclusive but not opposite are ().

A. There are at least 1 white balls, all of which are white balls. B there are at least 1 white balls and at least 1 red balls. C. There are just 1 white balls, and there are just two white balls. D there are at least 1 white balls, all of which are red balls.

Example 3. Two Go players, A and B, play chess in a match. The probability of A winning is 5% higher than that of B, and

2

The probability of chess is 59%, so the probability of B winning is _ _ _ _ _ _ _.

Example 4. If 1 card is randomly selected from 52 playing cards excluding big and small kings, The probability of drawing hearts (event A) is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _