1. Random events in life are divided into definite events and uncertain events, and definite events are divided into inevitable events and impossible events. Among them,
① The probability of inevitable events is 1, that is, p (inevitable events) =1;
② The probability of an impossible event is 0, that is, p (impossible event) = 0;
③ If A is an uncertain event, then 0
2. Calculation method of random event probability:
(1) theoretical calculation is divided into the following two cases:
The first type: the probability of random events involving only one-step experiment, such as: calculating a kind of probability model according to the relationship between the size and area of probability;
The second type: calculate the probability of random events involving two or more experiments by list method, enumeration method and tree diagram, such as matching purple, calculating whether the game is fair, etc.
② The experimental estimation is divided into the following two situations:
The first method: probability estimation through experiments. We should know that when the number of experiments is very large, the experimental frequency can be used as an estimate of the probability of events, that is, a large number of experimental frequencies are stable to the theoretical probability.
The second method: probability estimation through simulation experiment. For example, using a calculator to generate random numbers to simulate experiments.
To sum up, the available probability models can be roughly divided into three categories; The first kind of problem has no theoretical probability, and its estimated value can only be obtained through experimental simulation; Although the second kind of problem has theoretical probability, it is not available at present, and its estimated value can only be obtained by experimental simulation. The third kind of problem is simple classical probability, and it is easy to calculate its probability in theory.
It should be noted here that although we can use formulas to calculate probability, it is more important to understand the meaning of probability when learning this part of knowledge, rather than just strengthening the practice of applying formulas to calculate.
3. Do you know the application of probability?
By designing a simple probability model, we can make reasonable decisions under uncertainty. Probability is closely related to real life. Understand what is fair to both sides of the game, explain the fairness of the game in the language of probability, design the probability model of the game as required, and understand the relationship between probability and statistics in combination with specific practical problems, so that some practical problems can be solved. Examples of supplementary answers:
Answer the question:
1. There are two turntables that can rotate freely. Each turntable is divided into three equal sectors. Xiao Ming and Liang Xiao use them to match purple (red and blue can match purple). Do you think the probability of matching purple and not matching purple is the same?
2. A man is setting up a stall in the market. He saw a black bag in his hand, which contained 20 white balls with the same size, shape and quality, and each ball was written with a number (number 1-20). In addition, there are 1 red balls in the bag, and 2 1 red balls are all except colors. Rule: Touch only one ball at a time. Pay 1 yuan before touching, and write a number within 1-20. Touch the red ball for 5 yuan. The number touched is the same as the number written. The prize is 10 yuan.
Do you think this game is good for lottery winners? State your reasons.
(2) If a lottery winner wins many prizes, how much will he earn or lose each time? Answer supplementary answer questions reference answer:
1. method 1: list grids because
red
blue
blue
red
(red, red)
(red, blue)
(red, blue)
red
(red, red)
(red, blue)
(red, blue)
blue
(blue, red)
(blue, blue)
(blue, blue)
So p (matching purple) =5/9, p (matching purple) =4/9.
Method 2: enumeration method:
Because there are nine results of rotating dial, namely: (red, red), (red, blue), (red, blue), (red, red), (red, blue), (blue, red), (blue, blue), (blue, blue).
Method 3: Draw a tree diagram:
(red, red) (red, blue) (red, blue) (red, red) (red, blue) (red, blue) (blue, red) (blue, blue) (blue)
So p (matching purple) =5/9, p (matching purple) =4/9.
2.( 1) p (touching the red ball) = P (touching the ball with the same number) =1/21; Therefore, it is not good; (2) The average income for each time is
, so the average loss is 4/2 1 yuan.