Senior High School Mathematics Compulsory 3 Chapter 3 Probability Test Training
1. The following statement is true ()
A. The probability of any event is always between (0, 1). B. frequency exists objectively and has nothing to do with the number of tests.
C. With the increase of test times, the frequency will generally get closer to the probability d, which is random and cannot be determined before the test.
2. If you roll dice, the probability of throwing odd points is () A.B.C.D 。
3. Throw a coin with uniform texture. If you throw it 1000 times in a row, the probability of facing up for the 999th time is ().
A.B. C. D。
4. Take out three products from a batch of products, let A= "none of the three products are defective", B= "none of the three products are defective" and C= "none of the three products are defective", then the following conclusion is correct ().
A.a and c are mutually exclusive. B.B and c are mutually exclusive. C. Any two are mutually exclusive. No two are mutually exclusive.
5. If any badminton product is selected from a batch, the probability that its mass is less than 4.8g is 0.3, and the probability that its mass is less than 4.85 is ](g is 0.32, and the probability that its mass is in the range of [4.8,4.85] (g) is ().
A.0.62 B. 0.38 C. 0.02 D. 0.68
6. Throw two coins with uniform texture at the same time, and the probability of two heads facing up is ()
A.B. C. D。
7. If Party A and Party B stay in two vacant rooms at will, the probability of each party living in a room is ().
A. Boston center is uncertain
8. Randomly take two out of five genuine products and one defective product, and the probability of taking two out is exactly one genuine product and one defective product.
A. BC 1 year
9. There are two red balls and two white balls in a bag. Now take out 1 ball from the bag, then put it back in the bag and take out another ball. Then the probability that two balls are the same color is ().
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10. The existing five balls are marked as A, C, J, K and S, and are randomly placed in three boxes. Only one ball can be placed in each box, so the probability of K or S in the box is ().
A.B. C. D。
1 1, test five different genuine products and four different defective products of a product one by one until all the defective products are identified. If all the defective products are found after only five tests, such a detection method is ().
A.20 species B. 96 species C. 480 species D. 600 species
12. If the dice are thrown twice in a row, the points obtained respectively are M and N. If M and N are taken as the coordinates of point P, the probability that point P falls in this area is
A.B. C. D。
13. 10 Six men and five women should be selected to form a cheerleading team. If stratified sampling by sex, a boy is the group leader, and the number of different sampling methods is
A.B. C. D。
14.500ml of water has a paramecium. Now randomly take 2mL water sample from it and observe it under a microscope. The probability of finding paramecium is () A.0.5b.0.4c.0.004d Uncertainty.
15 As shown in the figure, if a handful of beans are randomly scattered in the figure, the probability of falling in the shaded part is ().
A.B. C. D。
16, mutual exclusion of two events is the () condition for the opposition of two events.
A. Sufficient and unnecessary B. Necessary and insufficient C. Sufficient and necessary D. Neither sufficient nor necessary
17. Among the following events, the number of random events is () ① If A and B are real numbers, then B+A = A+B; (2) June 65438+1 October1a northwest wind blows somewhere; ③ When x is a real number, x2 ≥ 0; ④ The attendance rate of a cinema is over 50%.
A. 1
18, choose Theory of Three Represents from A, B, C and D, then the probability that A is selected is ().
A.B. C. D。
19. There are ten cards marked 0 to 9 in a box. Choose a card from it, and the probability that the number on the card is not less than 6 is ().
A.B. C. D。
20. There are 10 small balls with the same size and shape in the box, including 8 white balls and 2 red balls, so the probability of taking 2 balls from them, at least 1 white ball, is () A.B.C.D
2 1. When A and B play chess, the probability of A winning is 30%, and the probability of a draw is 50%, so the probability of A losing is ().
A.30% B.20% C.80% D. None of the above is right.
22. If any point P is taken from the AB side of △ABC with an area of S, the probability that the area of △PBC is greater than ().
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23. If the points M and N obtained by continuous dice rolling twice are taken as the coordinates of point P, the probability that point P falls outside circle x2+y2=25 is
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24, from 1, 2, 3, 4, 5, 6 these six numbers, do not put back any two numbers, the probability that both numbers are even numbers is
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25, throwing three coins at the same time, then the opposite event is ().
A. at least 1 surface and at most 1 surface. B 1 face at most, exactly 2 faces.
C at most 1 face and at least 2 faces. D. At least 2 faces and exactly 1 face.
26. There are three girls and two boys in one group. Now, if a group leader is randomly selected from this group, the probability that one of the girls Xiaoli is elected as the group leader is _ _ _ _ _ _ _ _ _ _.
27. The probability that the sum of two dice is 3 is _ _ _ _ _ _ _ _ _ _ _.
28. A class committee consists of four boys and three girls, and now two of them are elected vice-monitor. At least 1 The probability of a girl being elected is _ _ _ _ _ _ _ _ _.
29. The probability of annual precipitation in western China is shown in the following table:
Annual precipitation/mm [100,150] [150,200] [200,250] [250,300]
The probability is 0.21.160.130.12.
Then the probability of annual precipitation in the range of [200,300] (m, m) is _ _ _ _ _ _ _ _
30. If a little P is thrown into △ABC with an area of S, the probability that the area of △PBC is less than _ _ _ _ _ _ _.
3 1 has five line segments, the lengths of which are 1, 3, 5, 7 and 9 respectively. If you choose any three of these five line segments, the probability that the selected three line segments can form a triangle is _ _ _ _ _.
32. In the isosceles Rt△ABC, if any point m is taken on the hypotenuse AB, the probability that the length of AM is less than the length of AC is _ _ _ _ _ _ _ _.
33, 10 different Chinese books and 2 different math books. What is the probability that you can come up with a math book by choosing two at random?
34. Box A has three balls in red, black and white, and Box B has two balls in yellow, black and white. Each box takes 1 ball. (1) Find the probability that two balls are different in color. (2) Please design a random simulation method to approximately calculate the probability that two balls in (1) have different colors (write the simulation steps).
35. As shown in the figure, two isosceles right triangles with a side length of 23cm are dug out from a square with a side length of 25cm.
The existing uniform particles are scattered in a square. What is the probability of particles falling in the middle band?
36. Seven students stand in a row in any order and try to find the probability of the following events:
(1) Event A: Edge; 2 event B: Sum is on the side; (3) Event C: Or on the side; (4) Event D: Neither sum is on the edge; (5) Event E: Right.
37. As shown in the figure, a square board with a side length of 16cm is hung on the wall, and small, medium and large are painted on it.
Three concentric circles with radii of 2 cm, 4 cm and 6 cm respectively. Someone stood 3 meters away and threw darts at the board.
When the dart hits the line or misses the board, it is not counted (it can be re-thrown). Q: (1) The probability of hitting the Great Circle.
how much is it? (2) What is the probability of a circle composed of a small circle and a middle circle being thrown? (3) make a big circle.
How much is the charge?
38. There is a 100 card (from 1 Tono. 100). Choose a card from it and calculate the multiple of: (1)7 to get how many cards? (2) The probability that the card number is a multiple of 7.
39. Four customers put their hats on the coat rack at will, and then each customer takes a hat at will, and ask (1) the probability that four people take their hats; (2) The probability of just three people holding their own hats; (3) The probability that people hold their own hats just 1; (4) The probability that four people don't hold their own hats.
40. Party A and Party B agreed to meet somewhere between six and seven o'clock, and the person who arrived first agreed to wait for another person for a quarter of an hour, and then they could leave when it was out of date, so as to find out the probability that they could meet.
Reference answer:
The title is 1 23455 6789 10.
Answer c b d b b c c a d
The title is11213141516171819 20.
Answer c a c b b d c a
Title 2 1 22 23 24 25
Answer c b b d c
26.27.28 29.0.25 30、 3 1、 32、
33. Solution: The total number of basic events is:12×11÷ 2 = 66. The number of basic events involved in the event of "being able to take out a math book" can be divided into two situations: (1) the basic events involved in "just taking out 1 math book". (2) "Take out two books full of math books" contains the basic number of events: 1. Therefore, the basic number of events included in the event "Can take out a math book" is: 20+ 1 = 2 1. So p ("can take out math books") =
34. Solution: (1) Let a = "The two balls taken out have the same color" and b = "The two balls taken out have different colors", then the probability of event A is: p (a) = =. Since event A and event B are opposite events, the probability of event B is:
P(B)= 1-P(A)= 1- =
(2) Step of random simulation: Step 1: Generate 1 ~ 3 and 2 ~ 4 groups of random numbers with integer values by lottery or computer (calculator), with n random numbers in each group. Use 1 to get the red ball, 2 to get the black ball, 3 to get the white ball and 4 to get the yellow ball. Step 2: Count the logarithm n of two groups of corresponding n pairs of random numbers, where two numbers in each pair are different. Step 3: Calculate the value. This is an approximation of the probability that the two balls are different in color.
35. Solution: Because the possibility of a uniform particle falling at any point in a square is equal, it meets the condition of geometric probability.
Let a = "particles fall in the middle banded area", then the square area is 25× 25 = 625, the areas of two isosceles right triangles are 2× 23× 23 = 529, and the banded area is 625-529 = 96, ∴p(a)= 1
36. Solution: (1); (2) ; (3) ;
(4) ; (5) 。
37. Solution: The area of the whole square plate, that is, the total area occupied by basic events, is.
We regard "falling into the great circle" as event A, "falling into the circle formed by the small circle and the middle circle" as event B, and "falling out of the great circle" as event C, so the area occupied by event A is: the area occupied by event B is: the area occupied by event C is.
(1) is derived from the probability formula of geometric probability; (2) ;
(3) 。
Comment: For the solution of (3), we can also directly apply the nature of opposing events to solve it.
38. Solutions: (1) have 7, 14, 2 1, …, 98, and * * *;
(2)P ("the card number obtained is a multiple of 7") =.
39. Solution: (1); (2) ; (3) ;
(4) 。
40. Solution: If X and Y respectively represent the time when Party A and Party B arrive at the agreed place, the necessary and sufficient conditions are as follows.
. Establish a rectangular coordinate system on the plane, as shown in the shaded part of the figure. This is a geometric probability problem, which consists of the probability formula of geometric probability,
Yes