Andrey chooses a three-digit number divisible by 33. Probability theory and statistics

(1 – 5). Andrey chooses three digit number. Find the probability that it is divisible by 33.

Solution:

n–number of three-digit numbers: 100; 101; 102; ...; 999

n = 999 – 99 = 900

m– the number of three-digit numbers that are multiples of 33

We get: k = 1; 2; 3; ...; thirty

Note: 33; 66; 99 are two-digit numbers, so: m = 30 – 3 = 27

Answer: 0,03

(6 – 10). Marina's TV is broken and only shows one random channel. Marina turns on the TV. At this time, two of the twenty channels show comedy films. Find the probability that Marina will end up on a channel where comedy is not shown.

Solution:

n= 20 – number of channels

m= 20 – 2 = 18 – number of channels where comedy is not shown

Answer: 0,9

(11 – 15). There are fifteen pies on the plate: 1 with meat, 4 with cabbage and 10 with cherries. Zhora chooses one pie at random. Find the probability that he ends up with meat.

Solution:

n= 15 – number of pies

m=1 – number of meat pies

Answer:

(16 – 20). At the taxi company this moment 20 cars available: 3 black, 3 yellow and 13 green. One of the cars, which happened to be closest to the customer, responded to the call. Find the probability that a yellow taxi will come to him.

Solution:

n= 20 – number of cars.

m=3 – number of cars yellow color

Answer:

(21 – 25). According to the terms of the promotion, every sixth can of coffee contains a prize. Prizes are randomly distributed among the pots. Valya buys a can of coffee in the hope of winning a prize. Find the probability that Valya will not find the prize in her jar?

Solution:

n= 6 – number of cans

m= 6 – 1 = 5 – number of cans where there is no prize

Answer:

(26 – 30). Sasha and dad decided to ride the Ferris wheel. There are a total of thirty booths on the wheel, of which 7 are blue, 17 are green, and the rest are red. Find the probability that Sasha will take a ride in the red booth.

Solution:

n= 30 – number of booths.

m= 30 – (7 + 17) = 6 – number of red booths

Answer:

(31 – 35). Grandma has 10 cups: 8 with red flowers, the rest with blue. Grandmother pours tea into a randomly selected cup. Find the probability that it will be a cup with blue flowers.

Solution:

n=10 – number of cups.

m= 10 – 8 = 2 – number of cups with blue flowers

Answer:

(36 – 40). There are 35 tickets for the exam. Stas didn't learn 7 of them. Find the probability that he will come across the learned ticket.

Solution:

n= 35 – number of tickets.

m= 35 – 7 = 28 – number of learned tickets

Answer: 0,8

(41 – 45). The parent committee purchased 27 puzzles for end-of-year gifts for children, 8 of them with paintings by famous artists and 19 with images of animals. Gifts are distributed randomly. Find the probability that Ksyusha will get a puzzle with an animal.

Solution:

n= 27 – number of puzzles

m= 19 – number of animal puzzles

Answer:

(46 – 50). On average, for every 150 flashlights, eighteen are faulty. Find the probability of buying a working flashlight.

Solution:

n= 150 – number of flashlights

m= 150 – 18 = 132 – number of working flashlights

Answer:

(51 – 55). On average, out of every 59 batteries sold, 56 batteries are charged. Find the probability that the purchased battery is not charged.

Solution:

n= 59 – number of batteries.

m= 59 – 56 = 3 – number of uncharged batteries

Answer:

(56 – 60). Arthur chooses a two-digit number at random. Find the probability that it ends in 7.

Solution:

m- quantity double digit numbers, ending in 7:17; 27; 37; ...; 97

n= 90 (number of two-digit numbers)

Answer: 0,1

(61 – 65). When an airplane is in level flight, the lift acting on the wings depends only on the speed. The figure shows this dependence for some aircraft. The abscissa axis shows speed (in kilometers per hour), and the ordinate axis shows force (in tons of force). Determine from the figure how much the lift force will increase (in tons of force) when the speed increases from 200 km/h to 400 km/h?

Solution:

Answer: for 3 tf

(66 – 70). The heater power in a car is regulated by an additional resistance that can be changed. In this case, the current strength changes in electrical circuit electric motor. The figure shows the dependence of the current on the resistance value. The abscissa axis shows the resistance (in Ohms), and the ordinate axis shows the current strength in Amperes. How many Amperes is the current in the circuit with a resistance of 0.5 ohms?

Solution:

Answer: 12 A

(71 – 75). The graph shows the dependence of engine torque on the number of revolutions per minute. The abscissa axis shows the number of revolutions per minute, and the ordinate axis shows the torque in Nm. How many more revolutions per minute will the engine make when the torque increases from 20 Nm to 140 Nm?

Solution:

Answer: at 1500 rpm

(76 – 80). The diagram shows the distribution of lands in the Ural, Volga, Southern and Far Eastern regions Federal districts by category. Determine from the diagram which district has the smallest share of agricultural land.

Solution:

The share of agricultural land is the smallest in the Far Eastern Federal District.

Andrey chooses a three-digit number. Find the probability that it is divisible by 33. Solution. How to calculate the number of all three-digit numbers? The first three-digit number is 100, the last is Total 900. All numbers that are divisible by 33 can be given by the formula 33N, where N is an integer. Let's find how many such numbers there are. To do this, let's solve the inequality: So, there are 27 such numbers in total. The probability is 27:900=0.03. Answer: 0.03 To answer this question, you need to divide the number of three-digit numbers divisible by 33 by the number of all three-digit numbers.

Andrey chooses a three-digit number. Find the probability that it is divisible by 10. Solution. How to calculate the number of all three-digit numbers? The first three-digit number is 100, the last is Total 900. All numbers that are divisible by 10 can be specified by the formula 10N, where N is an integer. Let's find how many such numbers there are. To do this, let's solve the inequality: So, there are 90 such numbers in total. The probability is 90:900=0.1. Answer: 0.1. To answer this question, you need the number of three-digit numbers divisible by 10 divided by the number of all three-digit numbers.

Kolya chooses a three-digit number. Find the probability that it is divisible by 4. Solution. How to calculate the number of all three-digit numbers? The first three-digit number is 100, the last is Total 900. All numbers that are divisible by 4 can be specified by the formula 4N, where N is an integer. Let's find how many such numbers there are. To do this, let's solve the inequality: So, there are 249:24=225 such numbers in total. The probability is 225:900=0.25. Answer: 0.25.

Kolya chooses a three-digit number. Find the probability that it is divisible by 93. Solution. How to calculate the number of all three-digit numbers? The first three-digit number is 100, the last is Total 900. All numbers that are divisible by 93 can be specified by the formula 93N, where N is an integer. Let's find how many such numbers there are. To do this, let's solve the inequality: So, there are 9 such numbers in total. The probability is 9:900=0.01. Answer: 0.01. To answer this question, you need to divide the number of three-digit numbers divisible by 93 by the number of all three-digit numbers.

Marina's TV is broken and only shows one random channel. Marina turns on the TV. At this time, eight out of forty channels show comedy films. Find the probability that Marina will end up on a channel where comedy is not shown. The probability is 32:40=0.8. Answer: 0.8. Solution. To answer the question of the problem, you need to divide the number of channels on which the comedy is not broadcast by total channels. 40-8 = 32 channels on which comedy is not broadcast. Total 40 channels.

Lyuba's TV is broken and only shows one random channel. Lyuba turns on the TV. At this time, twenty-five out of fifty channels show comedy films. Find the probability that Lyuba will end up on a channel where comedy is not shown. The probability is 25:50=0.5. Answer: 0.5. Solution. To answer the question of the problem, you need to divide the number of channels on which the comedy is not broadcast by the total number of channels = 25 channels on which the comedy is not broadcast. Total 50 channels.

Vasya’s TV is broken and only shows one random channel. Vasya turns on the TV. At this time, one channel out of twenty-one shows news. Find the probability that Vasya will end up on a channel where there is no news. The probability is 20:21 = Answer: Solution. To answer the question of the problem, you need to divide the number of channels on which news does not go by the total number of channels. 21-1=20 channels that do not carry news. There are 21 channels in total.

There are 10 pies on the plate: 3 with meat, 3 with cabbage and 4 with cherries. Sasha chooses one pie at random. Find the probability that he ends up with a cherry. The probability is 4:10=0.4. Answer: 0.4. Solution. To answer the question in the problem, you need to divide the number of cherry pies by total number pies.

There are 30 pies on the plate: 7 with meat, 17 with cabbage and 6 with cherries. Zhenya chooses one pie at random. Find the probability that he ends up with a cherry. The probability is 6:30=0.2. Answer: 0.2. Solution. To answer the question of the problem, you need to divide the number of cherry pies by the total number of pies.

There are seventeen pies on the plate: 2 with meat, 4 with cabbage and 11 with cherries. Yura chooses one pie at random. Find the probability that he ends up with meat. The probability is 2:17 = Answer: Solution. To answer the question of the problem, you need to divide the number of meat pies by the total number of pies.

The probability is 6:15=0.4. Answer: 0.4. Solution. To answer the question of the problem, you need to divide the number of yellow taxis by the total number of cars. The taxi company currently has 15 cars available: 3 black, 6 yellow and 6 green. One of the cars, which happened to be closest to the customer, responded to the call. Find the probability that a yellow taxi will come to him.

The probability is 99:100=0.99. Answer: 0.99. Solution. To answer the question of the problem, you need to divide the number of cans without a prize by the total number of cans. According to the terms of the promotion, every hundredth can of coffee contains a prize. Prizes are randomly distributed among the pots. Galya buys a can of coffee in the hope of winning a prize. Find the probability that Galya does not find the prize in her jar.

The probability is 8:18 = Answer: Solution. To answer the question of the problem, you need to divide the number of green taxis by the total number of cars. The taxi company currently has 18 cars available: 6 black, 4 yellow and 8 green. One of the cars, which happened to be closest to the customer, left when called. Find the probability that a green taxi will come to her.

The probability is 22:30 = Answer: Solution. To answer the question of the problem, you need to divide the number of green taxis by the total number of cars. The taxi company currently has 30 cars available: 3 black, 5 yellow and 22 green. One of the cars, which happened to be closest to the customer, left when called. Find the probability that a green taxi will come to her.

The probability is 5:6 = Answer: Solution. To answer the question of the problem, you need to divide the number of cans without a prize by the total number of cans. According to the terms of the promotion, every sixth can of coffee contains a prize. Prizes are randomly distributed among the pots. Valya buys a can of coffee in the hope of winning a prize. Find the probability that Valya will not find the prize in her jar?

The probability is (30-(24+3)):30=0.1. Answer: 0.1. Solution. To answer the question of the problem, you need to divide the number of red booths by the total number of booths. Vanya and dad decided to ride the Ferris wheel. There are a total of thirty booths on the wheel, of which 3 are blue, 24 are green, and the rest are red. The cabins take turns approaching the boarding platform. Find the probability that Vanya will ride in the red cab.

The probability is (19-(6+10)):19= Answer: Solution. To answer the question of the problem, you need to divide the number of orange booths by the total number of booths. Tema and dad decided to ride the Ferris wheel. There are nineteen booths in total on the wheel, of which 6 are blue, 10 are green, and the rest are orange. The cabins take turns approaching the boarding platform. Find the probability that Tema will ride in the orange car.

The probability is (25-3):25=22:25=0.88 Answer: 0.88. Solution. To answer the question of the problem, you need to divide the number of cups with blue flowers by the total number of cups. Grandma has 25 cups: 3 with red flowers, the rest with blue. Grandmother pours tea into a randomly selected cup. Find the probability that it will be a cup with blue flowers.

The probability is (17-5):17=12:17= Answer: Solution. To answer the question in the problem, you need to divide the number of cups with gold stars by the total number of cups. Grandfather has 17 cups: 5 with red stars, the rest with gold ones. Grandfather pours tea into a randomly selected cup. Find the probability that it will be a cup with gold stars.

The probability is (40-8):40=32:40=0.8. Answer: 0.8. Solution. To answer the question of the problem, you need to divide the number of learned tickets by the total number of tickets. There are 40 tickets in the exam, Senya did not learn 8 of them. Find the probability that he will come across the learned ticket.

The probability is (60-6):60=54:60=0.9. Answer: 0.9. Solution. To answer the question of the problem, you need to divide the number of learned tickets by the total number of tickets. There are 60 tickets in the exam, Stas did not learn 6 of them. Find the probability that he will come across the learned ticket.

The probability is 9:20=0.45. Answer: 0.45. Solution. To answer the question of the problem, you need to divide the number of puzzles with cars by the total number of puzzles. The parent committee purchased 20 puzzles for end-of-year gifts for children, 11 of them with cars and 9 with views of cities. Gifts are distributed randomly. Find the probability that Ilya will get the puzzle with the car.

The probability is 21:25=0.84. Answer: 0.84. Solution. To answer the question of the problem, you need to divide the number of puzzles with cars by the total number of puzzles. The parent committee purchased 25 puzzles for end-of-year gifts for children, 21 of them with cars and 4 with views of cities. Gifts are distributed randomly. Find the probability that Sasha will get the puzzle with the car.

The probability is (75-9):75=0.88. Answer: 0.88. Solution. To answer the question of the problem, you need to divide the number of working flashlights by the total number of flashlights. On average, for every 75 flashlights, nine are faulty. Find the probability of buying a working flashlight.

The probability is ():150=30:150=0.2. Answer: 0.2. Solution. To answer the question of the problem, you need to divide the number of batteries that do not work by the total number of batteries. On average, out of every 150 batteries sold, 120 batteries are charged. Find the probability that the purchased battery is not charged.

Andrey chooses a two-digit number at random. Find the probability that it ends in 5. Solution. How to calculate the number of all two-digit numbers? The first two-digit number is 10, the last Total is 99-9=90. All numbers that end in 5 can be given by the formula 10N+5, where N is an integer. Let's find how many such numbers there are. To do this, let's solve the inequality: So, there are 9 such numbers in total. The probability is 9:90=0.1. Answer: 0.1. To answer this question, you need to divide the number of two-digit numbers ending in 5 by the number of all two-digit numbers.

Vitya chooses a two-digit number at random. Find the probability that it starts with 9. Solution. How to calculate the number of all two-digit numbers? The first two-digit number is 10, the last Total is 99-9=90. There are 10 numbers that start with 9 (90, 91, 92,…,99). The probability is 10:90 = Answer: To answer this question, you need to divide the number of two-digit numbers that start with 9 by the number of all two-digit numbers.

Lesha chooses a two-digit number at random. Find the probability that it ends in 0. Solution. How to calculate the number of all two-digit numbers? The first two-digit number is 10, the last Total is 99-9=90. All numbers that end in 0 can be given by the formula 10N, where N is an integer. Let's find how many such numbers there are. To do this, let's solve the inequality: So, there are 9 such numbers in total. The probability is 9:90=0.1 Answer: 0.1. To answer this question, you need to divide the number of two-digit numbers ending in 0 by the number of all two-digit numbers.

No. 132821. Decision. Andrey chooses a three-digit number. Find the probability that it is divisible by 33. The probability is 27:900=0.03. Answer: 0.03. How to calculate the number of all three-digit numbers? The first three-digit number is 100, the last is 999. The total is 900. All numbers that are divisible by 33 can be given by the formula 33N, where N is an integer. Let's find how many such numbers there are. To do this, let's solve the inequality: So, there are 27 such numbers in total. To answer this question, you need to divide the number of three-digit numbers divisible by 33 by the number of all three-digit numbers.

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Algebra 9th grade

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