There are 4 pies on a plate. There are identical-looking pies on a plate

Job source: Decision 2653.-20. OGE 2017 Mathematics, I.V. Yashchenko. 36 options.

Task 18. The diagram shows the nutrient content of cottage cheese. Determine from the diagram which substances contain the least.

*Others include water, vitamins and minerals.

1) proteins; 2) fats; 3) carbohydrates; 4) other

Solution.

The smaller the sector on the pie chart, the less substance the product contains. In the problem you need to find the sector of the smallest size. This is a sector showing the carbohydrate content. We have answer number 3.

Answer: 3.

Task 19. There are identical-looking pies on the plate: 4 with meat, 10 with cabbage and 6 with cherries. Zhora takes one pie at random. Find the probability that the pie will contain cherries.

Solution.

Let's take the event that Zhora took the cherry pie. The number of favorable outcomes for event A is 6 (the number of cherry pies). Total outcomes 4+10+6=20 – total number of pies. Thus, the required probability is equal to:

Answer: 0,3.

Task 20. The formula tC = 5/9*(tF-32) allows you to convert the temperature value on the Fahrenheit scale to the Celsius scale, where tC is the temperature in degrees Celsius, tF is the temperature in degrees Fahrenheit. How many degrees on the Celsius scale does -4 degrees on the Fahrenheit scale correspond to?

Solution.

Let's substitute the value into the formula for converting from the Fahrenheit scale to the Celsius scale, and we get.

Main state exam OGE Mathematics task No. 9 Demo version 2018-2017 On the plate are pies that look identical: 4 with meat, 8 with cabbage and 3 with apples. Petya chooses one pie at random. Find the probability that the pie will contain apples.

Solution:

P = m / n = number of favorable outcomes / total number of outcomes

m = number of favorable outcomes = 3 (with apples)

n = total number of outcomes = 4 (with meat) + 8 (with cabbage) + 3 (with apples) = 15

Answer: 0.2

Demonstration version of the Main state exam OGE 2016 – task No. 19 Module "Real Mathematics"

The parent committee purchased 10 puzzles as gifts for children at the end of the year, including cars with city views. Gifts are distributed randomly. Find the probability that Misha will get the puzzle with the car.

Solution:

Answer: 0.3

Demonstration version of the Main state exam OGE 2015 – task No. 19 Module "Real Mathematics"

On average, out of 75 flashlights that go on sale, fifteen are faulty. Find the probability that a flashlight chosen at random in a store will turn out to be working.

Solution:

75 -total flashlights

15 - faulty

15/75=0.2 - probability that the flashlight will be faulty

1-0.2= 0.8 – probability that the flashlight will be working properly

Answer: 0.8

1. Vasya, Petya, Kolya and Lyosha cast lots as to who should start the game. Find the probability that Petya will start the game.

Favorable outcomes – 1.

Total outcomes – 4.

The probability that Petya will start the game is 1: 4 = 0.25

Answer. 0.25

2. The dice are thrown once. What is the probability that the number rolled is greater than 4? Round your answer to the nearest hundredth.

Favorable outcomes: 5 and 6. I.e. two favorable outcomes.

There are only 6 outcomes, since there are 6 sides on the die.

The probability that more than 4 points will be rolled is 2: 6 = 0.3333…≈ 0.33

Answer. 0.33

If the first digit discarded is 0,1,2,3 or 4, then the digit in front of it is not changed. If the first digit dropped is 5,6,7,8 or 9, then the digit in front of it is increased by 1.

3. In a random experiment, two dice are rolled. Find the probability that the total will be 8 points. Round your answer to the nearest thousand.

Favorable outcomes: (2;6), (6;2), (4;4), (5;3), (3;5). There are 5 favorable outcomes in total.

There are 36 total outcomes (6 ∙ 6).

Probability = 5: 36 = 0.138888…≈ 0.139

Answer. 0.139

4. In a random experiment, a symmetrical coin is tossed twice. Find the probability that heads will appear exactly 1 time.

There are two favorable outcomes: heads and tails, tails and heads.

There are four possible outcomes: heads and tails, tails and heads, tails and tails, heads and heads.

Probability: 2: 4 = 0.5

5. In a random experiment, a symmetrical coin was tossed three times. What is the probability of getting heads exactly twice?

The following favorable outcomes are possible:

When tossing a coin, heads come up with probability 0.5 and tails come up with probability 0.5. Therefore, the probability of getting the OOP combination is 0.5 ∙ 0.5 ∙ 0.5 = 0.125.

The probability of getting the OPO combination is 0.125.

The probability of getting the “ROO” combination is 0.125.

Therefore, the probability of favorable outcomes occurring is 0.125 + 0.125 + 0.125 = 0.375.

Answer. 0.375.

6. 4 athletes from Finland, 6 athletes from Russia and 10 athletes from the USA are participating in the shot put competition. Find the probability of that. that the athlete competing last will be from Russia.

4 + 6 + 10 = 20 (athletes) – total participants in the competition.

Favorable outcomes 6. Total outcomes 20.

The probability is 6: 20 = 0.3

7. On average, out of 250 batteries that go on sale, 3 are faulty. Find the probability that a randomly selected battery will be good.

Serviceable batteries: 250 – 3 = 247

Total batteries: 250

The probability is

Answer. 0.988

8. 20 athletes are participating in the gymnastics championship: 8 from Russia, 7 from the USA, the rest from China. The order in which the gymnasts perform is determined by lot. Find the probability that the athlete competing first is from China.

From China: 20 – 8 – 7 = 5 athletes

Probability:

Answer. 0.25

9. There are 16 teams participating in the World Championship. Using lots, they need to be divided into four groups of four teams each. There are cards with group numbers mixed in the box:

1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4.

Team captains draw one card each. What is the probability that the Russian team will be in the second group?

There are 4 teams in the second group, therefore there are 4 favorable outcomes.

There are 20 outcomes in total, since there are 20 teams.

Probability:

Answer. 0.25

10. The probability that a ballpoint pen writes poorly (or does not write) is 0.1. A buyer in a store chooses a pen. Find the probability that this pen writes well.

probability that the pen writes well + probability that the pen does not write = 1.

1 – 0.1 = 0.9 – probability that the pen writes well.

11. At the geometry exam, the student gets one question from the list. The probability that this is an inscribed circle question is 0.2. The probability that this is a question on the topic “Parallelogram” is 0.15. There are no questions that simultaneously relate to these two topics. Find the probability that a student will get a question on one of these two topics in the exam.

0,2 + 0,15 = 0,35

Answer. 0.35

12. In the trading floor, two identical machines sell coffee. The probability that the machine will run out of coffee at the end of the day is 0.3. The probability that both machines will run out of coffee is 0.12. Find the probability that by the end of the day there will be coffee left in both machines.

Probability that at least one machine will run out of coffee: 0.3 + 0.3 – 0.12 = 0.48 (0.12 is subtracted since this probability was taken into account twice when adding 0 and 0.3)

Probability that there will be coffee left in both machines:

1 – 0,48 = 0,52.

Answer. 0.52

13. A biathlete shoots at targets five times. The probability of hitting the target with one shot is 0.8. Find the probability that the biathlete hits the targets the first three times and misses the last two times. Round the result to hundredths.

4 times: 1 – 0.8 = 0.2

5 times: 1 – 0.8 = 0.2

Probability: 0.8 ∙ 0.8 ∙ 0.8 ∙ 0.2 ∙ 0.2 = 0.02048 ≈ 0.02

Answer. 0.02

14. There are two payment machines in the store. Each of them can be faulty with probability 0.05, regardless of the other machine. Find the probability that at least one machine is working.

Probability that both machines are faulty: 0.05 ∙ 0.05 = 0.0025

Probability that at least one machine is working:

1 – 0,0025 = 0,9975

Answer. 0.9975

15. There are 10 numbers on the telephone keypad, from 0 to 9. What is the probability that a randomly pressed number will be even?

Even numbers: 0, 2, 4, 6, 8. There are five even numbers.

There are 10 numbers in total.

Probability:

16. The competition of performers is held over 4 days. A total of 50 performances have been announced – one from each country. There are 20 performances on the first day, the rest are distributed equally between the remaining days. The order of performance is determined by lot. What is the probability that the Russian representative will perform on the third day of the competition.

Solution. 50 – 20 = 30 participants must perform within three days. Therefore, on the third day, 10 people perform.

Probability:

17. Lena throws the dice twice. In total, she scored 9 points. Find the probability that the second roll results in a 5.

There are four possible event events: (3;6), (6;3), (4;5), (5;4)

Favorable outcome one (4;5)

Probability:

Answer. 0.25

18. In a random experiment, a symmetrical coin is tossed twice. Find the probability that heads will appear exactly once.

Possible outcomes:

OR, RO, OO, RR

Favorable outcomes: OR, RO

On this page we will analyze a number of problems in probability theory about pies.

Problem 0D5CDD from the open bank of OGE tasks in probability theory

Task #1 (task number on fipi.ru - 0D5CDD). There are identical-looking pies on the plate: 4 with meat, 8 with cabbage and 3 with cherries. Petya takes one pie at random. Find the probability that the pie will contain cherries.

Solution:

Answer: the probability that the pie that Petya takes at random will end up with a cherry is 0.2.

Problem 8DEDED from the open bank of OGE tasks in probability theory

Task #2 (task number on fipi.ru - 8DEDED). There are identical-looking pies on the plate: 3 with cabbage, 8 with rice and 1 with onion and egg. Igor takes one pie at random. Find the probability that the pie will contain cabbage.

Solution: