"Using Frequency to Estimate Probability" PPT courseware for further understanding of probability

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"Using Frequency to Estimate Probability" PPT courseware for further understanding of probability

We know that when a coin is tossed, either heads or tails appear, and they are random. Through the above experiments, we found that the probability of heads appearing in a large number of experiments is 0.5, so what is the possibility of tails appearing?

The possibility of tails is also 0.5

This is why when we toss a coin, the probability of heads is 0.5 and the probability of tails is 0.5.

Although it cannot be determined in advance whether a random event occurs in an experiment, its occurrence shows a certain regularity in a large number of repeated experiments. The frequency of occurrence values ​​is close to a constant.

Random events and their probabilities

The definition of probability of event A:

Generally, when the same experiment is repeated in large numbers, the frequency of event A m/n (n is the number of experiments, m is the frequency of events) is always close to a certain constant, swinging around it, and then it is This constant is called the probability of event A, denoted as P(A)=P.

It can be seen from the definition:

(1) The basic method to find the probability of an event is through a large number of repeated experiments;

(2) Only when the frequency swings around a certain constant, this constant is called the probability of event A;

(3) Probability is the stable value of frequency, and frequency is the approximate value of probability;

(4) Probability reflects the likelihood of a random event occurring;

(5) The probability of a necessary event is 1, and the probability of an impossible event is 0. Therefore 0≤P(A)≤1.

It can be seen that the greater the likelihood of an event occurring, the closer the probability is to 1; conversely, the smaller the likelihood of an event occurring, the closer the probability is to 0.

Mathematics historical facts

People have found in long-term practice that in random experiments, due to the influence of many small accidental factors, although the results measured each time are not the same, the results obtained from a large number of repeated experiments can reflect objective laws. This is called big numbers law, also known as the law of large numbers.

Give the following conclusion, which one is wrong ( )

①If the chance of something happening is only one in 100,000, then it cannot happen.

②If the chance of something happening reaches 99.5%, then it will definitely happen.

③If something is not impossible, then it will definitely happen.

④If something is not inevitable, then it cannot happen.

A. 1 B. 2 C. 3 D. 4

Expand and improve:

1. Choose any letter in the English sentence "Wish you success!" (Wish you success!), the probability that this letter is "s" is ________.

2. Which of the following events has a probability of 0 ( )

A. Randomly toss an even coin twice, and at least one of them will land tails.

B. It will snow in Heilongjiang this winter

C. Roll two even dice at random. The sum of the points facing up is 1.

D. A turntable is divided into 6 sectors, arranged in red, white, white, red, red and white. Turn the turntable and the pointer stops in the red area.

summary

1. The concept of random events

Events that may or may not occur under certain conditions are called random events.

2. Definition of probability of random events

When the same experiment is repeated in large numbers, the frequency m/n of event A (n is the number of experiments, m is the frequency of events) is always close to a certain constant, swinging near it, then this constant is called The probability of event A is recorded as P(A)=P.

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Update Time: 2024-10-05

This template belongs to Mathematics courseware Beijing Normal University Ninth Grade First Volume Mathematics industry PPT template

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