There are 4 meat pies on the plate. On the plate are the same-looking pies

Quest 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, the content of which substances is the smallest.

*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 is contained in the product. In the problem, you need to find the sector of the smallest size. This is the sector showing the content of carbohydrates. We have the answer number 3.

Answer: 3.

Task 19. On the plate are the same-looking pies: 4 with meat, 10 with cabbage and 6 with cherries. Zhora randomly takes one pie. Find the probability that the pie will have a cherry.

Solution.

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

Answer: 0,3.

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

Solution.

Substitute in the conversion formula from Fahrenheit to Celsius the value , we get.

The main state exam OGE Mathematics assignment No. 9 Demo version 2018-2017 On the plate are pies, identical in appearance: 4 with meat, 8 with cabbage and 3 with apples. Petya randomly chooses one pie. Find the probability that the pie is filled with 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

Demo version of the Main State Examination of the OGE 2016 - task No. 19 Module "Real Mathematics"

The Parents' Committee purchased 10 puzzles for gifts to children by 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

Demo version of the Main State Examination of the OGE 2015 - task No. 19 Module "Real Mathematics"

On average, out of 75 flashlights sold, fifteen are faulty. Find the probability that a flashlight chosen at random in a shop is in good condition.

Solution:

75 total flashlights

15 - faulty

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

1-0.2= 0.8 - the probability that the flashlight will work

Answer: 0.8

1. Vasya, Petya, Kolya and Lyosha cast lots - who will start the game. Find the probability that Peter 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. A dice is 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.

Only 6 outcomes, since the dice has 6 faces.

The probability that more than 4 points will fall out is 2: 6 \u003d 0.3333 ... ≈ 0.33

Answer. 0.33

If the first discarded digit is 0,1,2,3 or 4, then the digit preceding it is not changed. If the first discarded digit is 5,6,7,8 or 9, then the digit before it is incremented by 1.

3. In a random experiment, two dice are rolled. Find the probability of getting 8 points in total. Round your answer to thousandths.

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

All outcomes 36 (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 it comes up heads 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 that heads will come up exactly twice?

The following favorable outcomes are possible:

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

The probability of getting the ORO combination is 0.125.

The probability of getting the combination "ROO" is 0.125.

Therefore, the probability of getting favorable outcomes 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 participate in the shot put competition. Find the probability of that. that the last athlete to compete 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 sold, 3 are defective. Find the probability that a randomly selected battery is good.

Serviceable batteries: 250 - 3 = 247

Total Batteries: 250

The probability is

Answer. 0.988

8. 20 athletes participate 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 who competes first is from China.

From China: 20 – 8 – 7 = 5 athletes

Probability:

Answer. 0.25

9. 16 teams participate in the World Championship. By drawing lots, they must be divided into four groups of four teams each. In the box are mixed cards with group numbers:

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. The buyer in the 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 - the probability that the pen writes well.

11. In 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 Parallelogram question is 0.15. There are no questions related to these two topics at the same time. Find the probability that the student will get a question on one of these two topics on 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 there will be coffee left in both machines by the end of the day.

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 coffee will remain in both vending 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 hit the targets the first three times and missed the last two. Round the result to the nearest hundredth.

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 a probability of 0.05, regardless of the other automaton. Find the probability that at least one automaton is serviceable.

The probability that both automata are faulty: 0.05 ∙ 0.05 = = 0.0025

Probability that at least one machine is in good condition:

1 – 0,0025 = 0,9975

Answer. 0.9975

15. There are 10 digits 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 in 4 days. There are 50 entries in total, one from each country. On the first day there are 20 performances, the rest are distributed equally among the remaining days. The order of performance is determined by lot. What is the probability that the performance of the representative of Russia will take place 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 rolls a dice twice. She scored 9 points in total. Find the probability of getting 5 on the second roll.

Four event events are possible: (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 it comes up tails exactly once.

Possible outcomes:

OR, RO, OO, RR

Favorable outcomes: RR, RO

We will analyze on this page a number of problems in the theory of probability about pies.

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

Task #1 (task number on fipi.ru - 0D5CDD). On the plate are the same-looking pies: 4 with meat, 8 with cabbage and 3 with cherries. Petya randomly takes one pie. Find the probability that the pie will have a cherry.

Solution:

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

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

Problem #2 (problem number on fipi.ru - 8DEDED). On the plate are the same-looking pies: 3 with cabbage, 8 with rice and 1 with onion and egg. Igor randomly takes one pie. Find the probability that the pie ends up with cabbage.

Solution: