This is correct, but wrong
Experts deservedly do not like tasks and puzzles at interviews. But we just love to solve such tasks for our own pleasure. What I personally don’t like is when you get the right answer, but at the same time your decision seems wrong to the author. I just want to show the solution of several popular similar problems that can be obtained in mind and without complicated calculations and compare them with the author’s correct ones.
Task 1. In a country where people want them to have only children-boys, each family continues to have children until a boy is born. If they have a girl, they have another child. If a boy, they stop. What is the ratio of boys and girls in such a country? (It is understood that the probability of having a boy is equal to the probability of having a girl, although, in fact, the ratio is 105: 100)
The right solution to this problem.
With probability 1/2 there will be one child - a boy.
With probability 1/4 there will be two children - a girl and a boy.
With a probability of 1/8 there will be three children - two girls and a boy.
...
With a probability of 1/2 ^ n there will be n children - (n-1) girls and a boy.
Mathematical expectation of the number of boys = 1
The mathematical expectation of the number of girls = 1/2 * 0 + 1/4 * 1 + 1/8 * 2 + 1/16 * 3 + ...
If the sum of this series is denoted by s, then it is easy to get that 2 * s - s = 1, s is 1, therefore, the ratio of boys and girls is 50:50.
And now the correct solution to this problem.
All schemes in the condition of this task are averting the eyes. There is a Great Rand, which gives a boy and a girl with the same probability, which means that the ratio will be 50:50.
If not convincing, I will explain. Someone plays a martingale in a casino, that is, puts on a color until it falls, doubling the stakes. From such behavior of the player (or players), the roulette will still produce the same number of black and red outcomes, exactly as the maternity hospital.
')
Task 2. Two companies sold coffee at the same price and volume. Both simultaneously held promotions: the first one started selling 15% more coffee, and the second one was 15% cheaper. Who started buying coffee more profitable?
The right solution to this problem.
If 100 ml of coffee cost 1 ruble before a stock, then after the first company 100 ml of coffee began to cost 100 * (100/115), which is approximately 87 kopecks, while the second obviously costs 85 or two kopecks cheaper.
And now the correct solution to this problem.
To divide by 115 in my mind, for example, is difficult. Therefore, it is possible to replace 15 with 50. In this case, the second company will receive twice as much coffee as a ruble, while the first will only get one and a half. The transition from 15 to 50 is legal with a percentage linearity.
Task 2 bis. What is more profitable: a contribution at 70% in a currency with inflation of 60%, or at 80% in a currency with inflation of 70%?
Task 3. Before you are two identical wine glasses. In one of them wine, in the other water. Scoop a teaspoon of water and pour it into a wine glass. How should stir. And then scoop a teaspoon of the mixture and pour it into a glass with water. What more: wine in a glass with water or water in a glass with wine?
The right solution to this problem.
1. Suppose that in a drinker there are 100 parts of a liquid, and in a spoon - 10 parts
2. Take 10 parts of water from a wine glass and pour it into a wine glass with wine and mix
3. In a wine glass with wine 110 parts of the liquid. And in a spoonful of the mixture from this glass one by one eleventh of the volume of water and wine. Consequently, 9 whole and 1/11 parts of wine and 10/11 parts of water are contained in a spoonful of the mixture. All this is poured into a glass with water
4. Now in the glass with water 90 whole and 10/11 parts of water and 9 whole and 1/11 part of the wine, which in total gives 100 parts of the liquid
5. In the wine glass with 90 whole and 10/11 parts of wine and 9 whole and 1/11 parts of water, which in total also amounts to 100 parts of the liquid.
6. Equivalent exchange
And now the correct solution to this problem.
Do not count the parts and how to stir. Whatever manipulations take place, the entire volume withdrawn is replaced with the same amount. And that's all.
Bonus Tasks that are quickly and correctly solved. I present you the pleasure to solve them yourself.
1. Last Friday, the girl Masha first went to the club and met 20 new people. This Friday she went to the club, met 10 old acquaintances and met 10 new people. How many new people will Masha most likely meet next Friday?
2. A convex polyhedron casts a pentagonal shadow. What is the minimum number of faces he has?
3. A triangle that does not have obtuse angles is called acute. How to place twelve points in three-dimensional space, so that they are the vertices of the greatest number of acute triangles? How many acute triangles come out?
4. You and another stranger are asked to make a natural number. If your numbers match, then you get a prize. What number will you make?
5. In the box with cookies is a liner. To win, you need to collect a complete collection of different liners, for this the average consumer buys 72 boxes. How many different inserts in the complete collection?
6. How thick should the coin be (in radii) so that the probability of falling on an edge is equal to the probability of an eagle falling out?
Task 1. In a country where people want them to have only children-boys, each family continues to have children until a boy is born. If they have a girl, they have another child. If a boy, they stop. What is the ratio of boys and girls in such a country? (It is understood that the probability of having a boy is equal to the probability of having a girl, although, in fact, the ratio is 105: 100)
The right solution to this problem.
With probability 1/2 there will be one child - a boy.
With probability 1/4 there will be two children - a girl and a boy.
With a probability of 1/8 there will be three children - two girls and a boy.
...
With a probability of 1/2 ^ n there will be n children - (n-1) girls and a boy.
Mathematical expectation of the number of boys = 1
The mathematical expectation of the number of girls = 1/2 * 0 + 1/4 * 1 + 1/8 * 2 + 1/16 * 3 + ...
If the sum of this series is denoted by s, then it is easy to get that 2 * s - s = 1, s is 1, therefore, the ratio of boys and girls is 50:50.
And now the correct solution to this problem.
All schemes in the condition of this task are averting the eyes. There is a Great Rand, which gives a boy and a girl with the same probability, which means that the ratio will be 50:50.
If not convincing, I will explain. Someone plays a martingale in a casino, that is, puts on a color until it falls, doubling the stakes. From such behavior of the player (or players), the roulette will still produce the same number of black and red outcomes, exactly as the maternity hospital.
')
Task 2. Two companies sold coffee at the same price and volume. Both simultaneously held promotions: the first one started selling 15% more coffee, and the second one was 15% cheaper. Who started buying coffee more profitable?
The right solution to this problem.
If 100 ml of coffee cost 1 ruble before a stock, then after the first company 100 ml of coffee began to cost 100 * (100/115), which is approximately 87 kopecks, while the second obviously costs 85 or two kopecks cheaper.
And now the correct solution to this problem.
To divide by 115 in my mind, for example, is difficult. Therefore, it is possible to replace 15 with 50. In this case, the second company will receive twice as much coffee as a ruble, while the first will only get one and a half. The transition from 15 to 50 is legal with a percentage linearity.
Task 2 bis. What is more profitable: a contribution at 70% in a currency with inflation of 60%, or at 80% in a currency with inflation of 70%?
Task 3. Before you are two identical wine glasses. In one of them wine, in the other water. Scoop a teaspoon of water and pour it into a wine glass. How should stir. And then scoop a teaspoon of the mixture and pour it into a glass with water. What more: wine in a glass with water or water in a glass with wine?
The right solution to this problem.
1. Suppose that in a drinker there are 100 parts of a liquid, and in a spoon - 10 parts
2. Take 10 parts of water from a wine glass and pour it into a wine glass with wine and mix
3. In a wine glass with wine 110 parts of the liquid. And in a spoonful of the mixture from this glass one by one eleventh of the volume of water and wine. Consequently, 9 whole and 1/11 parts of wine and 10/11 parts of water are contained in a spoonful of the mixture. All this is poured into a glass with water
4. Now in the glass with water 90 whole and 10/11 parts of water and 9 whole and 1/11 part of the wine, which in total gives 100 parts of the liquid
5. In the wine glass with 90 whole and 10/11 parts of wine and 9 whole and 1/11 parts of water, which in total also amounts to 100 parts of the liquid.
6. Equivalent exchange
And now the correct solution to this problem.
Do not count the parts and how to stir. Whatever manipulations take place, the entire volume withdrawn is replaced with the same amount. And that's all.
Bonus Tasks that are quickly and correctly solved. I present you the pleasure to solve them yourself.
1. Last Friday, the girl Masha first went to the club and met 20 new people. This Friday she went to the club, met 10 old acquaintances and met 10 new people. How many new people will Masha most likely meet next Friday?
2. A convex polyhedron casts a pentagonal shadow. What is the minimum number of faces he has?
3. A triangle that does not have obtuse angles is called acute. How to place twelve points in three-dimensional space, so that they are the vertices of the greatest number of acute triangles? How many acute triangles come out?
4. You and another stranger are asked to make a natural number. If your numbers match, then you get a prize. What number will you make?
5. In the box with cookies is a liner. To win, you need to collect a complete collection of different liners, for this the average consumer buys 72 boxes. How many different inserts in the complete collection?
6. How thick should the coin be (in radii) so that the probability of falling on an edge is equal to the probability of an eagle falling out?
Source: https://habr.com/ru/post/246979/
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