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"Stability of Frequency" Frequency and Probability PPT Courseware 2
learning target
1. Experience the process of experiments, statistics and other activities, and further develop the awareness and ability of cooperation and communication during the activities;
2. Understand that when the number of tests is large, the test frequency is stable at the theoretical probability, and the probability of a certain event can be estimated based on this.
New course introduction
In the investigation, the number of times each object appears is called _________, and the ratio of the number of times each object appears to the total number of times is called _________.
A certain event may or may not occur under the same conditions. The quantity indicating the probability of occurrence is called _________.
Talk about it
In Chapter 9 of "Mathematics (Volume 2 for Grade 7)", students already know what random phenomena are and what the probability of an event in random phenomena is. Do you still remember?
1. What is random phenomenon?
Under the same basic conditions, different results may occur. Which result occurs depends on "chance" and is accidental. This type of phenomenon is called random phenomenon.
2. Can you give examples of random phenomena?
When you toss a coin, the result may be heads or tails. This is a random phenomenon.
When Xiao Ming rides to school, the time spent on the road may be 20 minutes, or 18 minutes, or 21 minutes... This is a random phenomenon.
3. What is a random event? Can you give an example?
Things that may happen in random phenomena are called random events.
For example, in the random phenomenon of tossing a coin, heads is a random event and tails is another random event.
4. What is the probability of a random event?
In random phenomena, the probability of an event occurring can be characterized by a non-negative real number not exceeding 1. This number is called the probability of the event.
Toss an even coin. After the coin falls, there will be two situations: (1) Heads up (2) Heads down. Do you think the probability of heads up and heads down is the same?
1. Two people at the same table play a coin tossing game 20 times, and record the data in the table below
2. Accumulate the experimental results of the whole class and fill in the summary of experimental data in the table below.
3 Based on the table above, complete the line chart in the table below.
4. Observing the line chart, what patterns did you find?
Think about it:
What is the value range of the probability P(A) of event A? inevitable event
What is the probability of it happening, what is the probability of an impossible event happening?
Discuss
Based on the above experiment, please estimate the probabilities of heads up and heads down when tossing an even coin. Are they equal?
in conclusion
In random phenomena, whether a random event will occur or not cannot be predicted in advance.
It seems irregular on the surface, but when we repeat the experiment in large numbers, the frequency of this event appears to be stable.
Therefore, after doing a lot of experiments, the frequency of an event can be used as an estimate of the probability of the event.
The connection and difference between probability and frequency:
Connection: When the number of trials is large, the frequency of an event is stable near the corresponding probability, that is, the trial frequency is stable at the theoretical probability. Therefore, the probability of an event can be estimated by using the frequency of an event through multiple trials.
Difference: The probability of a certain possible event occurring is a fixed value. The frequency of this event fluctuates. When the number of trials is not large, the difference between the frequency and probability of the event is even large. The frequency of an event cannot simply be equated to its probability. It is necessary to use the frequency of an event to estimate the probability of an event through multiple experiments.
Practice in class
1. The toy store run by Xiaoying’s mother once received a box of 3,000 plastic balls in black and white. In order to estimate how many balls of each color there were, she mixed the balls in the box and randomly took them out. She recorded the color of a ball and put it back into the box. After repeating the above process many times, she found that the frequency of touching black balls fluctuated around 0.7. Based on this, she could estimate that the number of black balls was approximately _________.
2. Which of the following statements is correct ( )
A. The probability of an event occurring is , which means: in two repeated experiments, one of them must occur
B. There are 100 balls in a bag. Xiao Ming touched it 8 times. Each time he only touched the black ball and no white ball. Conclusion: There are only black balls in the bag.
C. Two one-yuan coins are tossed at the same time. Possible situations include:
① Both coins are heads; ② Both coins are tails; ③ One head and one tail. Therefore, the probability of one head and one tail is 1/3.
D. There are 400 classmates in the whole grade, and there will definitely be two people who have birthdays on the same day.
Summary of this lesson
What did you and your peers gain from today’s study?
1. Use the conditions and methods of frequency estimation probability and apply the above content to solve some practical problems.
2. On the surface, every observation of a random phenomenon is accidental, but if you observe a random phenomenon multiple times, you can immediately find that there are inevitable laws among a large number of accidents.
Operation
Must do: Toss an even coin, and the probability of landing heads is 1/2. So, if you toss the coin 100 times, can you guarantee that it will land heads exactly 50 times? communicate with peers
Choice: Roll an even die,
(1) What possible results will occur?
(2) Is each outcome equally likely? How did you do it?
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