"Probability of Random Events" PPT

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"Probability of Random Events" PPT

Part One: Learning Objectives

1. Master the concepts of random events, inevitable events, and impossible events.

2. Correct understanding of the meaning of probability.

3. Understand the relationship between frequency and probability.

New course introduction

problem situation

Does burning wood produce heat?

Will the earth still rotate tomorrow?

Can the cooked duck escape?

Will the stone be weathered within a day at normal temperatures?

What are the characteristics of each of these events whether they occur or not?

(1) "The earth keeps turning"

(2) "Wood burns and produces energy"

(3) "At normal temperatures, stones weather within a day."

(4) "Someone shoots once and hits the target."

(5) "Flip a coin and it comes up heads"

(6) "Snow melts at standard atmospheric pressure and when the temperature is below 0°C"

Probability of random events PPT, part 2: learning new knowledge

(1) Necessary events, impossible events, random events

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

Necessary events: Events that must occur under certain conditions are called inevitable events.

Impossible event: An event that is impossible to occur under certain conditions is called an impossible event.

Deterministic events and random events are collectively called events, generally represented by capital letters A, B, C...

(2) The definition and understanding of probability

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.

Probability of random events PPT, Part 3: Frequency and Probability

1. Definition of frequency

Under the same conditions, n trials are conducted. In these n trials, the number of times event A occurs is called the frequency of event A.

The ratio na/n is called the frequency of event A, and is recorded as fn(A).

2. Definition of probability

When the same experiment is repeated in large numbers, the frequency fn(A) of event A is always close to a certain constant and swings near it. At this time, this constant is called the probability of event A.

The relationship between frequency and probability

(1) Connection: As the number of trials increases, the frequency will swing near the probability and tend to be stable.

In practical problems, if the probability of an event is unknown, frequency is often used as its estimate.

(2) Difference: The frequency itself is random and cannot be determined before the test. The frequency of events obtained by repeated tests of the same number or different times may be different.

Probability is a certain number that exists objectively and has nothing to do with each trial.

Note the following points:

(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 the event;

(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

Probability of random events PPT, Part 4: Homework

① If three products are randomly selected from 12 similar products (10 of which are genuine and two are defective), which of the following events is an inevitable event ( )

A. All three are genuine B. At least one is defective

C. All three are defective D. At least one is genuine

② If n repeated experiments are performed under the same conditions to obtain the frequency f(n) of an event A, then as n increases, there is ( )

A.f(n) is equal to a certain constant B.The difference between f(n) and a certain constant gradually decreases

C.The absolute value of the difference between f(n) and a certain constant gradually decreases

D.f(n) swings around a certain constant and tends to be stable

③ There are 4 white balls and 5 black balls in the box. Take out any ball from them.

(1) What is the event of "the yellow ball was taken out"? What is the probability?

(2) What is the event of "the white ball was taken out"? What is the probability?

(3) What is the event of "the white ball or the black ball was taken out"? What is the probability?

Probability of random events PPT, Part 5: Summary after class

1. ① Understand the concepts of inevitable events, impossible events, and random events;

② Understand the meaning of frequency and frequency.

2. Necessary events, impossible events, and random events occur under certain conditions. When conditions change, the nature of the event also changes.

3. Random events show regularity when a large number of experiments are conducted under the same conditions, and the frequency is always close to the constant P(A). P(A) is called the probability of the event.

4. Necessary events and impossible events can be regarded as two special cases of random events. Therefore, the probability of any event occurring satisfies: 0≤P(A)≤1.

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Update Time: 2024-07-04

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