"Estimating Probability Using Frequency" PPT courseware

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"Estimating Probability Using Frequency" PPT courseware

Part One: Do it

(1) Toss an even coin 400 times. Every 50 times, record the number of "heads" and "tails" respectively. After summarizing the data, complete the following table:

(2) Based on the data in the table above, draw a line statistical chart in the figure to represent the frequency of "heads up":

(3) In the picture, use a red pen to draw a straight line indicating the frequency of 1/2. What did you find?

(4) The following table is the experimental data of coin tossing conducted by some mathematicians in history. Do these data support the pattern you discovered?

It can be seen that as the number of coin tosses increases, the frequency of "heads" stabilizes at about 1/2.

It seems reasonable to use frequency to estimate the probability of a coin landing "heads".

The above example shows that through a large number of repeated experiments, the frequency of a random event can be used to estimate the probability of that event.

Using frequency to estimate probability PPT, part 2: example analysis

For example, the production of ceramic tiles is affected by the firing time, temperature, and material. When a brick is fired in a furnace, it may become a qualified product, a defective product, or a waste product. Which result will occur?

It cannot be predicted before firing, so this is a random phenomenon, and the result of firing is a "qualified product" is a random event. The probability of this event is called the "qualified product rate". Since the firing result is not equally possible, How often do we commonly use “qualified products”?

As an estimate of "good product rate".

A ceramic tile factory conducted quality inspections on a large number of recently released ceramic tiles of a certain model. The results are as follows:

(1) Calculate each frequency of qualified products in the table above (accurate to 0.001);

(2) Estimate the qualified product rate of this ceramic tile (accurate to 0.01);

(3) If the factory produces 500,000 tiles of this model this month, try to estimate the number of qualified products.

Solution: (1) Calculate item by item and fill in the table as follows:

(2) Observing the above table, we can find that when the number of tiles sampled is n ≥ 400, the frequency of qualified products is stable around 0.962, so we can take p = 0.96 as an estimate of the qualified product rate of this type of tiles.

(3) 500000×96%=480000 (blocks),

It can be estimated that the number of qualified products of this model is 480,000 pieces.

Using frequency to estimate probability PPT, part 3: practice

The picture shows a turntable that can rotate freely. The surface of the turntable is divided into 8 identical sectors, and the colors are divided into three types: red, yellow, and blue. The pointer of the turntable is fixed, and the turntable is allowed to rotate freely. When it stops, write down where the pointer points. Color. Repeat this 50 times and record the results in the table below:

(1) Try to estimate the probability that when the disk stops, the pointer points to yellow?

(2) If the disk is freely rotated 240 times, approximately how many times will the pointer point to yellow?

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Update Time: 2024-10-19

This template belongs to Mathematics courseware Hebei Education Edition Ninth Grade Mathematics Volume 2 industry PPT template

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