"Estimating Probability Using Frequency" Probability Preliminary PPT

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"Estimating Probability Using Frequency" Probability Preliminary PPT

The first part: the famous teacher’s eye-catching

Knowledge point 1: The relationship between frequency and probability

The frequency of a random event can be used to estimate its probability, but probability ≠ frequency.

Knowledge point 2: Use frequency to estimate probability

For general random events, when doing a large number of repeated tests, as the number of tests increases, the frequency of an event always swings around a fixed number, showing a certain degree of stability. Therefore, the frequency of a random event can be used to estimate its probability through a large number of repeated experiments.

[Typical example] There are 20 balls in two colors, red and yellow, in an opaque bag. Each ball is exactly the same except for its color. A certain learning interest group did a ball touch test. After mixing the balls, they randomly picked out a ball. After writing down the color, they put it back into the bag and repeated it. The following table is some statistical data during the experiment

(1) Complete the above table;

(2) The estimated value of the probability of "touching the red ball" is ________; (accurate to 0.1)

(3) Try to estimate the number of red balls in the bag.

Analysis: (1) Divide the number of times the red ball is touched by the number of times the ball is touched to obtain the frequency of touching the red ball; (2) The constant that the frequency of a large number of repeated tests stabilizes can be used as an estimate of the probability; (3) ) The number of red balls can be obtained by multiplying the obtained probability of touching the red ball by the total number of balls.

Answer: (1) Fill in the table from left to right with 0.64 and 0.58.

(2)0.6

(3) It is estimated that there are about 20×0.6=12 red balls in the bag.

Use frequency to estimate probability PPT, part 2: basic pass

1. In a large number of repeated experiments, regarding the frequency and probability of random events, which of the following statements is correct ()

A. Frequency is probability

B. Frequency has nothing to do with the number of trials

C. Tests are conducted under the same conditions. If the number of tests is the same, the frequency values ​​obtained by each test group will also be the same.

D. As the number of trials increases, the frequency will generally gradually stabilize near the probability value.

2. The data obtained by Xiao Ming and his classmates from the "Tossing a Coin with a Uniform Texture Test" is as follows:

Number of throws 100 200 300 400 500

Frequency of heads up 53 98 156 202 244

If the number of coin tosses is 1000, then the frequency of "heads" is closest to ()

A. 20 b． 300

C. 500 D. 800

3. In an opaque bag, there are several red balls and 4 yellow balls. They have no difference except their color. After shaking, randomly take out a ball from it, write down the color and put it back into the bag. Through a large number of repeated ball touching experiments, it is found that the frequency of touching yellow balls is 0.2, then it is estimated that there are approximately red balls in the box ()

A. 16 B． 20

C. 25 D． 30 pieces

4. [Liaoning Panjin High School Entrance Examination] An opaque box contains a ball that is identical except for color. There are only 6 white balls in it. If each time the balls are thoroughly mixed, a ball is picked out at random and the color is recorded before being put back into the box. After a large number of repeated tests, it is found that the frequency of touching white balls is stable at about 20%, then the value of a is about _ _______.

Using frequency to estimate probability PPT, part three: ability improvement

6． The figure shows the results of a computer simulation of randomly throwing a thumbtack.

There are three inferences below:

① When the number of throws is 500, the number of times the computer records "nail tip up" is 308, so the probability of "nail tip up" is 0.616;

② As the number of tests increases, the frequency of "nail tip upward" always swings around 0.618, showing a certain stability. It can be estimated that the probability of "nail tip upward" is 0.618;

③If the computer is used to simulate this test again, then when the number of throws is 1000, the frequency of "nail tip upward" must be 0.620.

The reasonable one is ()

A. ① B. ②

C. ①② D. ①③

Using frequency to estimate probability PPT, part 4: thinking training

10． The quality inspection results of a certain batch of table tennis balls are as follows:

Number of table tennis balls drawn n 200 500 1000 1500 2000

Frequency of excellent products m 188 471 946 1426 1898

Excellent product frequency m/n 0.940 0.942 0.946 0.951 0.949

(1) What is the estimated probability of this batch of "excellent" table tennis balls? (accurate to 0.01)

(2) Select 5 yellow balls, 13 white balls, and 22 red balls from this batch of table tennis balls. They are all the same except for color, and put them into an opaque bag.

Keywords: Free download of PPT courseware for mathematics in the first volume of the ninth grade of People's Education Edition, PPT download of estimating probability using frequency, preliminary PPT download of probability, .PPT format;

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Update Time: 2024-10-15

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