Dominant release

There are three cards with the same shape, size and color, marked with the numbers "1", "2" and "3" respectively. For the second time, randomly select one card from these three cards and write down the number. Please draw a tree diagram to show all the possible results of the above experiment, and find the probability that the number taken for the second time is greater than the number taken for the first time.

02

Analysis:

From the words "write down the numbers and put them back" in the title, we can know that this title belongs to "put them back explicitly" The event in this topic is to touch the card twice. By looking at the number of the card, it can be determined that the event includes two links. Touch the first card, put it back, and then touch the second card, so the tree diagram should be drawn in two layers.

The number of the first card may be one of three, such as 1, 2, 3, so the first layer should draw three crosses;

In the second draw, the number of the second ball may be one of three, so the second layer should be connected with the three forks of the first layer, and each small branch has three forks.

Draw a tree diagram, let * * * get 3× 3 = 9 cases, find out the case that the number extracted for the second time is greater than the number extracted for the first time, and then find out the probability.

03

Dominant irreversibility

An opaque cloth bag contains four ping-pong balls with the same size and texture, and the numbers 1, -2, 3 and -4 are marked on the spherical surface respectively. Xiao Ming first randomly draws a ball from the bag (does not put it back), and then randomly draws a second table tennis ball from the remaining three balls.

(1)*** There are several possible results;

(2) Please draw a tree diagram to find the probability that the product of two table tennis numbers is even.

04

Analysis:

This topic belongs to "dominant non-return". The event in this topic is to touch two ping-pong balls and look at the numbers of the ping-pong balls. It can be determined that the event contains two links, so the tree diagram should be drawn in two layers. The number of the first ping-pong ball may be one of four, such as 1, -2, 3, -4, so four crosses should be drawn on the first floor. Because it has not been put back, the number of the second ping-pong ball may be one of the remaining three, so it is necessary to connect the four forks on the second floor and the first floor, and there are three forks on each twig to draw a tree diagram.

05

Intangible return

Xiaoming rode his bike from home to school and passed three intersections with red and green lights. Assuming that the probability that he meets a red light and a green light at every intersection is zero, what is the probability that Xiao Ming just meets a red light when passing through these three intersections? Please use a tree diagram to explain.

06

Analysis:

Through repeated analysis, it is easy to make mistakes. The problem is actually equivalent to a pocket with 1 red balls and 65438 green balls, which are randomly taken three times where they are put back. The event in this question is that Xiao Ming rode his bike from home to school and passed through three intersections with red lights and green lights, so it can be determined that the event includes three links, so the tree diagram should be drawn on three levels. Because every intersection may be a red light, the tree diagram should be drawn in three layers.

07

Can't see it, can't put it back.

Xiaoming has three pens, red, blue and black. There are two erasers, white and gray. Xiao Ming randomly took out 1 pen and used it with 1 eraser. He tried to list all possible results with a tree diagram or table, and found out the probability of taking out a red pen and a white eraser.

08

Analysis:

A little analysis from the text shows that this problem belongs to "hiding without putting it back", and the objects chosen are pens and erasers. The event in this question is that Xiao Ming has three pens: red, blue and black. The two erasers are white and gray. Take out 1 pen and 1 eraser to use together. From this, it can be determined that the event contains two links, so the tree diagram should be drawn in two layers. As for which pen and eraser to take first, you can be arbitrary without affecting the result. The key is to draw the bifurcation of each layer correctly.

09

There are two calculators with different shapes (A and B respectively) and their matching protective covers (A and 6 respectively) scattered on the table (as shown in the picture). If two calculators and protective sleeves are randomly selected, the probability of exact matching can be obtained by tree diagram method or list method.

10

Analysis:

I learned from the article that this topic belongs to "hiding without putting it back", and it is easy to make mistakes when choosing objects at will without specifying whether it is a calculator or a protective case. The events in this topic are randomly selected from the calculator and the protective case, which seems to be a perfect match. From this, it can be determined that the event includes two links, the first is to take it, not put it back, and then the second is to take it, so the tree diagram should be drawn in two layers. The first layer may be a, b, a, and then look at the second layer. Because it has not been put back, the second layer may be one of the remaining three, so the second layer should be connected with four branches of the first layer, and three more branches should be added to each small branch to draw a tree diagram.