"Probability of Events" PPT courseware

Description

"Probability of Events" PPT courseware

learning target

1. Understand the meaning of probability, initially use frequency to estimate probability, and understand the connection and difference between probability and frequency.

2. Through a large number of experiments, it is felt that as the number of experiments increases, the frequency of a random event always swings around a fixed number, showing a certain stability. The frequency can be used to estimate the probability.

Knowledge review: inevitable events, impossible events, random events

Examine whether the following events can occur?

(1) Conductors generate heat when energized;

(2) Stones thrown upward will fall;

(3) Water will boil when the temperature rises to 100°C under standard atmospheric pressure.

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

Examine whether the following events can occur?

(1) Seeds germinate in a vacuum without moisture;

(2) Steel melts under normal temperature and pressure;

(3)3+5≥10

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

Examine whether the following events can occur?

(1) Someone hits the target once with a shot;

(2) Marin can win the Beijing Olympics men’s table tennis singles championship;

(3) The number of points that appears when a dice is thrown is an even number.

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

Thinking and solving doubts:

Since random events are uncertain, on the surface it seems that chance is dominant and there is no inevitability. However, after long-term practice and in-depth research, people found that although random events are uncertain in terms of the results of each test, they show a completely certain regularity in a large number of repeated experiments.

experiment one:

Ask the students to divide into groups of four to do the experiment of tossing a penny.

Requirement: Choose a classmate and toss a coin 10 times to choose a classmate.

Record the number of heads (m) and finally use the formula m/n (n=10) to calculate the result of heads and complete the following table:

Experiment 2: Computer tossing coins

Thinking 1: What conclusion can you draw from the above two experiments?

When the number of coin tosses is large, the frequency value of heads is stable, close to the constant 0.5, and swings around it

Thinking 2: What conclusions can you draw from this experiment?

When there are a large number of balls for random inspection, the frequency m/n of high-quality items is close to the constant 0.95 and swings around it.

Thought 3: The above experiments show that it is unpredictable whether a random event will occur in each trial, but after a large number of repeated experiments, as the number of trials increases, the frequency of event A shows a certain regularity. This regularity How is it reflected?

The frequency of events is relatively stable, swinging around a certain constant.

The relationship between frequency and probability

(1) Connection: As the number of trials increases, the frequency will swing near the probability and become 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 differs from each time. The test has nothing to do with it.

Generally, the possibility of an event occurring can be expressed by a number. We call this number the probability of the event occurring, usually denoted as P (event). When conducting a large number of repeated tests, as the number of tests increases, the frequency of a random event always fluctuates around the probability of the event, showing a certain degree of stability. The frequency of event occurrence can thus be used to estimate the probability of an event occurring.

Class exercises:

Throw a cube with six faces marked 1, 2, 3, 4, 5, and 6. After it settles,

(1) Is it likely that the number on the upward side of the cube is "5"?

(2) If "4" does not come up after five tosses, will "4" definitely come up after the sixth toss?

Summary of this lesson

Generally, the possibility of an event occurring can be expressed by a number. This number is called the probability of the event occurring.

When conducting a large number of repeated experiments, as the cumulative number of experiments increases, the frequency of a random event always fluctuates around the probability of the event, showing a certain stability, so that the frequency of the event can be used to estimate the probability of the event. Probability.

The difference and connection between frequency and probability

1. The frequency itself is random and cannot be determined before the test. The frequency of events obtained by repeating the same number of tests will be different.

2. Probability is a certain number, which is independent of each trial. It is a quantity used to measure the likelihood of an event occurring.

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Update Time: 2024-10-18

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