• Caesar_v roztin
• Calendar chips
• Blood tests
• Sleepy period
• Preparing for the fall

How to signify the imovirnіst vipadannya. Imovirnіst podії

Selecting the correct bet to lie down is less likely due to intuition, sports knowledge, bookmaker odds, and also due to the odds ratio. Possibility to raise a similar indicator for betting is a surety for success in predicting future future, on which bets are transferred.
The bookmakers have three types of coefficients (reported by the stats), depending on the variety of deposits, as a way to improve the profitability of the engraving.

Decimal coefficients

Rozrahunok ymovirnosti podії u razі vіdbuvaєtsya for the following formula: 1/coef.sob. = v.i, de coef.ob. - Coefficient of subdivision, and v.i - imovirnist result. For example, we take the odds of winning 1.80 at a rate of one dollar, zdіysnyuyuchi mathematical diyu for the formula, we take the graves, scho imovіrnіst result podії for the version of the bookmaker 0.55 vіdsotka.

Fractional coefficients

For varying fractional coefficients, the formula for rozrahunka ymovirnosti will be different. So, with a coefficient of 7/2, the first number means a possible increase in the net profit, and the other, the increase in the necessary rate, for taking away the profit, equals such a rank: Here zn.coef is the standard of the coefficient, chs.coef is the number of the coefficient, v.i is the imovirnist result. In this way, for the fractional odds 7/2, the ratio looks like 2/(7+2) = 2/9 = 0.22, and 0.22 is similar to the result of the match for the version of the bookmaker's office.

American odds

American coefficients are not very popular among gravitationalists and, as a rule, they are exclusively in the United States, with a complicated and tangled structure. For the type of nutrition: “How to improve the ability to move in such a way?”, it is required to designate that such coefficients can be negative and positive.

The coefficient with the sign "-", for example, -150, shows that for the withdrawal of a net profit of 100 dollars, it is necessary to raise a rate of 150 dollars. Imovirnіst podії razrakhovuєtsya vhodyachi z formulas de nebіbly dividing the negative coefficient by the sum of the negative coefficient i 100. Looking at the application of the rate -150, so (-(-150)) / ((-(-150)) + 100) = 150 / (150 + 100) \u003d 150/250 \u003d 0.6, de 0.6 multiplied by 100 and the result of the flexibility of the subdivision becomes 60 weave. The formula itself is suitable for positive American coefficients.

Would you like to know, what are the mathematical chances for the success of your bet? Here are two good news for you. Persha: to protect the passage, it is not necessary to carry out folded windows and stained glass windows large number hour. Dosit skoristatisya with simple formulas, a robot with some kind of loan kіlka hvilin. Friend: after reading these articles, you will easily be able to secure the passage, be it yours.

In order to correctly determine the passage, it is necessary to complete three steps:

• Razrahuvati percent ymovirnosti result podії on the idea of ​​the bookmaker's office;
• Calculate the ymovirnist for statistical data independently;
• Identification of the value of the rate with an eye on the offense of change.

Look at the report of the skin from the krokiv, zastosovuchi like a formula, and apply it.

The first crochet - it is necessary to know, with some kind of assessment of the chances for the next result, the bookmaker himself. Adzhe realized that it was not so easy to bet odds at a bookmaker's office. For whom we coriste with this formula:

PB=(1/K)*100%,

de R B - Imovirnist result on the bookmaker's opinion;

K - BC coefficient for the result.

Supposedly, to win the London Arsenal in the fight against Bavaria, the coefficient is 4. Tse means that the ability of this victory to BC is equal to (1/4) * 100% = 25%. Abo Djokovic is playing against Pivdenny. For Novak's victory, the multiplier is 1.2, which has a chance to increase (1/1.2) * 100% = 83%.

So evaluate the chances for the success of skin engraving, that team itself BC. Having created the first crochet, we move on to another.

Rozrahunok ymovirnosti under grave

Another point of our plan is the official assessment of the imovirnosti podії. If we can mathematically correct such parameters as motivation, game tone, then we will speed up the simplified model and we will be more corrosive with the statistics of the front teeth. For the analysis of the statistical stability of the result, the formula is fixed:

PІ\u003d (rozum / M) * 100%,

dePІ- ymovіrnіst podії on the thought of grave;

ROZUM - the number of successful matches, which had such a match;

M - total number of matches.

Shchob was zrozumіlіshe, let's put it on. Endi Murray and Rafael Nadal played together 14 matches. 6 of them have recorded total under 21 in games, 8 have total over. It is necessary to recognize the possibility that the upcoming match will win the total over: (8/14) * 100 = 57%. Valencia played at the Mestal against Atlético in 74 matches, which won 29 wins. Immovable victory over Valencia: (29/74) * 100% = 39%.

I don’t know everything about the statistics of the previous games! Naturally, as for a new team, if such a chance to win is not seen, then such a betting strategy is better for matches, for which super players are no better. Now we are able to determine the bookmaker’s own fluency of results, and we have all the knowledge to go to the rest of the time.

Determining the value of the bet

The value (valuation) of the pair and the passage may be without a middle link: the greater the value, the greater the chance for a pass. The value is secured as follows:

V=PІ*K-100%,

de V - value;

P І - ymovіrnіst result on better's thought;

K - BC coefficient for the result.

Admittedly, we want to put Milan on the win in the match against Romi and they cheered up that the red-blacks had a 45% chance of winning. The bookmaker gives us the result with a coefficient of 2.5. Chi bude so parі tsіnnim? We carry out rosary: ​​V \u003d 45% * 2.5-100% \u003d 12.5%. Miraculously, we have before us a price bet with good chances for a pass.

Let's take another fall. Maria Sharapova plays against Petri Kvitova. We want to lay down the favor for the help of Mary, ymovіrnіst yakoї, for our rozrahunkami, 60%. kontori proponuyut tsey result multiplier 1.5. Valuity is indicated: V = 60% * 1.5-100 = -10%. Like Bachimo, the value of the rate does not show, and in the face of it, it will disappear.

Imovirnist pass rate: vysnovok

When rozrahunku prokhіdnostі rates mi vykoristali simple model, as it is based on statistics. For the sake of perfection, it is necessary to protect a rich variety of factors, as in skin sports individually. Buvaє, scho itself is not a statistical factor and may have a larger injection. Without which it would be a mustache, it would simply be overdone. Having chosen your niche, you will soon learn to respect all the nuances and give a more accurate assessment of the dampness of the undertones, including a lot of other infusions. Golovne, love those that you are engaged in, step by step rush forward and move your mastery step by step. Good luck and success to the hoary world of betting!

"Vipadkovostі not vipadkovі"... To sound like this, no matter what the philosopher said, but on the other hand, the share of the great science of mathematics. In mathematics, the theory of imovirnosti deals with differences. Formulas and apply the task, as well as the main designations of science will be presented in the article.

What is the theory of imovirnosti?

The theory of imovirnosti is one of the mathematical disciplines, as it develops vipadkovi podії.

Sob it was a little bit more mindful, a small butt was aimed: if you throw a coin uphill, you can fall “eagle” or “tails”. As long as the coin is being rebuyed, it is possible to offend you. Tobto mozhlivіst mozhlivih naslіdkіv svіvіdnositsya 1:1. If you draw one from a deck of 36 cards, then the same ymovirnist will be indicated like 1:36. It would have been better if there was nothing to add and rebuff, and even more so with additional mathematical formulas. Prote, as if repeating the same song a lot of times, it is possible to reveal the regularity and її bases to predict the result of the subdivisions for other minds.

To sum up everything that has been said above, the theory of imovirnosti in a classically logical sense can be blamed on one of the possible subdivisions of a numerical value.

Three sides of history

The theory of imovirnosti, formulas and applications of the first tasks appeared even in the distant Middle Ages, if earlier winicks try to predict the results of card games.

On the other hand, the theory of imovirnosti is not small with anything related to mathematics. Vaughn was grounded by empirical facts and by the power of the undertaking, which could be done practically. The first works in this sphere as a mathematical discipline appeared in the 17th century. The founders were Blaise Pascal and Pier Fermat. A trivaly hour of stench played gambling and chanted the songs of laws, about how they blew the roses of prosperity.

The same methodology is used by Christian Huygens, although he did not know about the results of Pascal's and Fermat's investigations. The concept of “theory of immovability”, formulas and applications that are respected by the first in the history of the discipline, was introduced by him himself.

The work of Jacob Bernoulli, Laplace's and Poisson's theorems are of great importance. They developed the theory of imovirnosti more similar to the mathematical discipline. Its current form of the theory of immovability, the formulas and applications of the main tasks took the edge off Kolmogorov's axioms. As a result of all the changes, the theory of imovirnost became one of the mathematical divisions.

Basic understanding of the theory of immovability. Podії

To the head understanders of the discipline є "pod_ya". There are three views:

• Reliable. Tі, scho v_dbudutsya at any vpadku (coin in the fall).
• Impossible. Podії, scho not vydbudutsya for the current layout (the coin will lose its hang in the poіtrі).
• Vipadkov. Tі, scho will be chi will not be. The stench can be thrown in by various officials, and it’s even more important to talk like that. If you talk about a coin, then it is a change factor that can affect the result: the physical characteristics of the coin, its shape, external position, the strength of the throw.

The mustache under the butts is indicated by the great Latin letters, krim P, which is another role. For example:

• A = "The students came to the lecture."
• = = "students didn't come to the lecture".

For practical tasks, it is customary to write down in words.

One of the most important characteristics podіy - їх equivalence. Tobto toss a coin, all options for a weekend fall are possible, until it falls out. And yet, they are not equally strong. Tse vіdbuvaєtsya, if htos specially vplyvaє on the result. For example, "targeted" grave cards or brushes, in some places the center of gravity.

More podії buvayut crazy and insane. Sums of subdivision do not include one by one. For example:

• A = "the student came to the lecture".
• B = "student came to the lecture".

Qi podії nezalezhnі one of the one, and the appearance of one of them does not flow into the appearance of the other. Nesumsnі podії vynachayutsya tim, scho one including the appearance of another. If you talk about that very coin, then the “tails” dropping makes it impossible for the “heads” to appear in this experiment.

Climb over the coffins

Podії can be multiplied and folded, obviously, logical links “І” and “ABO” are introduced in the discipline.

The amount is determined by the time that you can show up either A, or B, or two at the same time. Like the stench is unimaginable, the remaining option is unimaginable, vipade either A or B.

Multiple podіy polagaє in the appearance of A and at the same time.

Now it is possible to introduce a sprinkling of examples, so that the basics, the theory of imovirnosti and formulas are remembered better. Apply the solution of tasks given.

Head 1: The company is taking part in the competition for the award of contracts for three different jobs.

• A \u003d "the firm revokes the first contract."
• A 1 = "the firm does not withdraw the first contract".
• B = "firm takes another contract".
• Y 1 = "the firm does not withdraw another contract"
• Z = "the company withdraws the third contract".
• З 1 = "the firm does not withdraw the third contract".

For help, we will try to overcome the following situations over the pods:

• K = "the firm takes away all contracts".

A mathematical looker has the following look: K = ABC.

• M = "the firm does not take away the agreement."

M \u003d A 1 B 1 Z 1.

Convenience task: H = "the firm takes one contract". It is not clear what kind of contract the company takes (the first, the other or the third), it is necessary to write down the whole series of possible subdivisions:

H \u003d A 1 ND 1 υ AB 1 Z 1 υ A 1 B 1 C.

A 1 BC 1 - a series of subdivisions, de firm does not take the first and third contract, but takes another. Vіdpovіdnym method zapisanі іnshі mozhlivі podії. The symbol υ in the discipline denotes the link "ABO". If you want to translate the guidance of the butt of a human being, then the firm takes away either the third contract, or the other, or the first. With a similar rank, you can enroll other minds in the discipline "Theory of Immorality". The formulas that apply the solution of the tasks presented above will help to grow independently.

Vlasne, imovirnist

Perhaps, in this mathematical discipline, the imovirnistness of the subdivision is the central understanding. Іsnuє 3 ways of imovirnosti:

• more classical;
• more statistical;
• more geometric.

The skin may have a place in the nursery. The theory of imovirnosti, formulas and applications (grade 9) are mostly classically designed, as it sounds like this:

• Imovirnist situatsii A more expensive increase in the number of results, which should be taken її appearing, to all possible results.

The formula may look like this: P(A)=m/n.

A - vlasne, podium. If it is a vypadok, protella A, yoga can be written down as A or A 1.

m - the number of possible pleasant moods.

n - all the subs, which can be.

For example, A = "draw a card of the heart's suit". A standard deck has 36 cards, 9 of them are of the heart suit. Vidpovidno, the formula for the solution of the problem looked like:

P(A) = 9/36 = 0.25.

The result has the ability to draw a card of the hearts suit from the deck, stock 0.25.

To higher mathematics

Now it has become a little obvious that such a theory of imovirnosti, formulas that apply the virishennya task that are used in the school program. The proteo theory of imovirnosti is also being developed in other mathematics, as it is in universities. Most often, they operate with geometric and statistical design theories and folding formulas.

Duzhe tsіkava theory of imovіrnostі. The formulas and applications (the most important thing in mathematics) are more likely to start from the small - from the statistical (abo frequency) designation of fluency.

Statistical pidkhіd is not super-simple to classical, but expands yogo. If in the first moment it was necessary to signify, with what kind of imovirnistu the podia will become, then in what method it is necessary to indicate, as often it will be necessary. Here, a new concept of “visible frequency” is introduced, so that Wn(A) can be known. The formula is nothing like the classical one:

Although the classical formula is calculated for forecasting, it is statistically based on the results of the experiment. Take, for example, a little task.

Vіddіl technological control pereviryaє virobi akіst. Among 100 votes, 3 inaccuracies were found. How to know the frequency of a particular product?

A = "appearance of a new product".

W n (A) \u003d 97/100 \u003d 0.97

Otzhe, the frequency of the same product becomes 0.97. The stars took 97? Three 100 products, which were misinterpreted, 3 turned out to be inaccurate. Від 100 zabiraєmo 3, otrimuєmo 97, ce kіlkіst yakіsnogo goods.

Trochs about combinatorics

Another method of the theory of imovirnosti is called combinatorics. Yogo's main principle lies in the fact that, as a sing-song choice, you can create m different ways and choosing B - in n different ways, then choosing A and B can be done in a multiplier way.

For example, from place A to place B, there are 5 roads. From the place B to the place C there are 4 ways. In how many ways can you get from place A to place C?

It's simple: 5x4 = 20, so there are twenty different ways to get from point A to point C.

Let's ease the task. What are some ways to arrange cards in solitaire? The deck has 36 cards - the main exit point. To recognize the number of ways, it is necessary to see the exit points on one card and multiplier.

Tobto 36x35x34x33x32 ... x2x1 = the result does not fit on the calculator screen, so you can simply calculate 36! Sign "!" beating numbers shows that the whole series of numbers is multiplied by each other.

The combinatorialists have the same understanding, like a permutation, a placement that one day. The skin makes its own formula from them.

The orderings of the set of elements are called distributions. Placement can be repeated, so that one element can be won over a few times. І without repetition, if the elements are not repeated. n - all elements, m - elements, yakі take part in the placement. The formula for placement without repeating matime viglyad:

A n m =n!/(n-m)!

Z'ednannya z n elements, yakі vіdrіznyayutsya less order of placement, called a permutation. Mathematics can see: Рn = n!

By one of n elements, we call such elements, in which it is important, as if there were elements and how many of them are common. Mathime viglyad formula:

A n m =n!/m!(n-m)!

Bernoulli formula

Theoretically, ymovirnosti, like in skin disciplines, є pracіvіdatnyh in their galusi doslednikіv, yakі vyveli її new equal. One of these practices is Bernoulli's formula, which allows you to recognize the imovirnist appearance of a singing voice for independent minds. It is not worth talking about those that appeared A in the experiment did not lie down, either appeared, or appeared tієї well podії in the early stages or advanced trials.

Rivnyannia Bernoulli:

P n (m) = C n m × p m × q n-m.

Imovirnist (p) appearance under (A) is invariable for skin testing. The imaginativeness of the fact that the situation will occur exactly m times in a number of experiments will be calculated by the formula, which is presented more. Obviously, blame the power, how to recognize the number q.

Like a podia And the time is now, the number of times, apparently, it may not come. One is the whole number, as it is accepted to designate all the traces of the situation in the discipline. To that, q is a number, which means the possibility of a bad weather.

Now you see Bernoulli's formula (theory of imovirnosti). Apply the rozvyazannya of tasks (the first rіven) razglyadno far away.

Task 2: Inform the store to make a purchase from the immovirnistyu 0.2. 6 people came to the store directly. What is the possibility of making a purchase?

Solution: Shards are unknown, scalable sills can make a purchase, one thing is all six, it’s necessary to check all possible possibilities, cory with Bernoulli’s formula.

A = "confirm purchase".

In my opinion: p = 0.2 (as assigned to the manager). Obviously, q = 1-0.2 = 0.8.

n = 6 (socks at the store 6 ventilators). The number m can be changed from 0 (the buyer is expected not to make a purchase) to 6 (everyone in the store can buy). The result takes a decision:

P 6 (0) \u003d C 0 6 × p 0 × q 6 \u003d q 6 \u003d (0.8) 6 \u003d 0.2621.

Zhodin z kupts_v not zdіysnyt zdіysnіt zіymіvіrіstyu 0,2621.

How does Bernoulli's formula (theory of imovirnosti) win? Apply the rozvyazannya tasks (another riven).

After the induced butt, I will blame the food about those who went to C і r. What is the number in step 0 of a good unit. Schodo C, then yoga can be known by the formula:

C n m = n! /m!(n-m)!

The scores for the first application are m = 0, obviously, C = 1, which adds the result to the principle. Vykoristovuyuchi new formula, we try to find out, what is the possibility of buying goods by two people.

P 6 (2) = C 6 2 ×p 2 ×q 4 = (6×5×4×3×2×1) / (2×1×4×3×2×1) × (0.2) 2 × (0.8) 4 = 15 × 0.04 × 0.4096 = 0.246.

The theory of imovirnosti is not so foldable. Bernoulli's formula, applied as presented above, is a direct confirmation of this.

Poisson formula

Rivnyannia Poisson wins for the calculation of small-scale vipadkovyh situations.

Basic formula:

P n (m) = m /m! × e (-λ) .

When tsiomu = n x p. The axis is such a simple Poisson formula (theory of imovirnosti). Apply rozv'yazannya tasks razglyadno distance.

Manager 3: 100,000 parts were produced at the factory. Defective part = 0.0001. What is the likelihood that there will be 5 defective parts in the batch?

Like a bachimo, a schlyub - tse small imovirna podia, in connection with which the Poisson formula (the theory of imovirnosti) is victorious for calculation. Apply the solution of similar tasks, they are not considered in any way in other disciplines, the necessary data are introduced into the formula:

A \u003d "the detail will be defective in a vipadkovo way."

p = 0.0001

n = 100000 (number of parts).

m = 5 (defective parts). Submit the data in the formula and take it:

R 100000 (5) = 105/5! X e -10 = 0.0375.

So just like Bernoulli's formula (the theory of imovirnosti), apply a decision for the help of what is written higher, Poisson's equal may not be known. In essence, yoga can be known by the formula:

e -λ = lim n -> ∞ (1-λ/n) n .

Prote є special tables, from which they may change all the values.

De Moivre-Laplace theorem

As for Bernoulli’s scheme, the number of tests is large, and the number of times the number of tests appears is the same for all schemes, then the number of times the number of times in the series of tests can be known by the Laplace formula:

Р n (m) = 1/√npq x ϕ(X m).

Xm = m-np/√npq.

To better remember Laplace's formula (theory of imovirnosti), apply the task to help below.

On the other hand, we know X m, substituting data (the stink of everything indicated above) in the formula, we take 0.025. For an additional table, the number ϕ (0.025) is known, the value of which is 0.3988. Now you can submit all data to the formula:

P 800 (267) \u003d 1 / √ (800 x 1/3 x 2/3) x 0.3988 \u003d 3/40 x 0.3988 \u003d 0.03.

Thus, the efficiency of the fact that an advertising leaflet is used exactly 267 times becomes 0.03.

Bayes formula

Bayes formula (theory of imovirnosti), apply a dream for help, which will be brought lower, equal, like describing the imovirnіst podії, spiraling on the furnishing, yakі could buti pov'yazanі with him. The basic formula may look like this:

P (A | B) \u003d P (B | A) x P (A) / P (B).

And і є singing podіyami.

Р(А|B) - intellectual imovirnіst, so it can be the status of A for understanding that the subdivision is true.

P (B | A) - the mental capacity of the subject of V.

Also, the last part of the short course "Theory of Immorality" is the Bayesian formula, apply the solution of problems below.

Head office 5: Phones from three companies were brought to the warehouse. With which part of the phones that are manufactured at the first plant, it will be 25%, at another - 60%, at the third - 15%. It seems that the average number of defective samples at the first factory is 2%, another - 4%, and the third - 1%. It is necessary to know the reliability of the fact that if the phone vibrates, it will turn out to be defective.

A = "vipadkovo takes the phone."

1 has a telephone, which was prepared by the first factory. Vіdpovіdno, za'yavlyatsya v 2 i v 3 (for other and third factories).

The result takes:

P(1)=25%/100%=0.25; P(2) = 0.6; Р(В 3) = 0.15 - this is how we know the emo- rnіst of the skin variant.

Now it is necessary to know the smartness of the product, so that the quality of defective products from firms:

P(A/B1)=2%/100%=0.02;

P (A / B 2) \u003d 0.04;

P(A/B3) = 0.01.

Now we can imagine the Bayesian formula and take it away:

P(A) = 0.25 x 0.2 + 0.6 x 0.4 + 0.15 x 0.01 = 0.0305.

The article presents the theory of imovirnosti, formulas and applications of the highest order, but rather the tip of the iceberg of great discipline. After all that has been written, it is logically motivated, what is the need for the theory of immovability in life. Simple people well-formed advice, it is better to ask about it from the one who has helped you more than once by hitting the jackpot.

Would you like to know, what are the mathematical chances for the success of your bet? Here are two good news for you. Persha: in order to protect the passage, it is not necessary to carry out folded clothes and stained glass for a rich hour. Dosit skoristatisya with simple formulas, a robot with some kind of loan kіlka hvilin. Friend: after reading these articles, you will easily be able to secure the passage, be it yours.

In order to correctly determine the passage, it is necessary to complete three steps:

• Razrahuvati percent ymovirnosti result podії on the idea of ​​the bookmaker's office;
• Calculate the ymovirnist for statistical data independently;
• Identification of the value of the rate with an eye on the offense of change.

Look at the report of the skin from the krokiv, zastosovuchi like a formula, and apply it.

The first crochet - it is necessary to know, with some kind of assessment of the chances for the next result, the bookmaker himself. Adzhe realized that it was not so easy to bet odds at a bookmaker's office. For whom we coriste with this formula:

PB=(1/K)*100%,

de R B - Imovirnist result on the bookmaker's opinion;

K - BC coefficient for the result.

Supposedly, to win the London Arsenal in the fight against Bavaria, the coefficient is 4. Tse means that the ability of this victory to BC is equal to (1/4) * 100% = 25%. Abo Djokovic is playing against Pivdenny. For Novak's victory, the multiplier is 1.2, which has a chance to increase (1/1.2) * 100% = 83%.

So evaluate the chances for the success of skin engraving, that team itself BC. Having created the first crochet, we move on to another.

Rozrahunok ymovirnosti under grave

Another point of our plan is the official assessment of the imovirnosti podії. If we can mathematically correct such parameters as motivation, game tone, then we will speed up the simplified model and we will be more corrosive with the statistics of the front teeth. For the analysis of the statistical stability of the result, the formula is fixed:

PІ\u003d (rozum / M) * 100%,

dePІ- ymovіrnіst podії on the thought of grave;

ROZUM - the number of successful matches, which had such a match;

M - total number of matches.

Shchob was zrozumіlіshe, let's put it on. Endi Murray and Rafael Nadal played together 14 matches. 6 of them have recorded total under 21 in games, 8 have total over. It is necessary to recognize the possibility that the upcoming match will win the total over: (8/14) * 100 = 57%. Valencia played at the Mestal against Atlético in 74 matches, which won 29 wins. Immovable victory over Valencia: (29/74) * 100% = 39%.

I don’t know everything about the statistics of the previous games! Naturally, as for a new team, if such a chance to win is not seen, then such a betting strategy is better for matches, for which super players are no better. Now we are able to determine the bookmaker’s own fluency of results, and we have all the knowledge to go to the rest of the time.

Determining the value of the bet

The value (valuation) of the pair and the passage may be without a middle link: the greater the value, the greater the chance for a pass. The value is secured as follows:

V=PІ*K-100%,

de V - value;

P І - ymovіrnіst result on better's thought;

K - BC coefficient for the result.

Admittedly, we want to put Milan on the win in the match against Romi and they cheered up that the red-blacks had a 45% chance of winning. The bookmaker gives us the result with a coefficient of 2.5. Chi bude so parі tsіnnim? We carry out rosary: ​​V \u003d 45% * 2.5-100% \u003d 12.5%. Miraculously, we have before us a price bet with good chances for a pass.

Let's take another fall. Maria Sharapova plays against Petri Kvitova. We want to lay down the favor for the help of Mary, ymovіrnіst yakoї, for our rozrahunkami, 60%. kontori proponuyut tsey result multiplier 1.5. Valuity is indicated: V = 60% * 1.5-100 = -10%. Like Bachimo, the value of the rate does not show, and in the face of it, it will disappear.

Imovirnist pass rate: vysnovok

When rozrahunku prokhіdnostі rates mi vykoristali simple model, as it is based on statistics. For the sake of perfection, it is necessary to protect a rich variety of factors, as in skin sports individually. Buvaє, scho itself is not a statistical factor and may have a larger injection. Without which it would be a mustache, it would simply be overdone. Having chosen your niche, you will soon learn to respect all the nuances and give a more accurate assessment of the dampness of the undertones, including a lot of other infusions. Golovne, love those that you are engaged in, step by step rush forward and move your mastery step by step. Good luck and success to the hoary world of betting!

There will be a task for an independent vision, before which you can look at the views.

The setting of the problem is glaring: to find out the qualities of the current podias, but it is necessary to calculate the imovirnosti of the other podias, as well as the similarities with the given podias. In tsikh zavdannya vinikaє nebhіdnіst іt іѕ dіyah іmovіrnosti, yak davannya that mnozhennya ymovіrnosti.

For example, two shots were made on the field. Podia A- getting into pitching from the first post, hitting B- Hit from another postril. Todi sum podіy Aі B- Hit from the first or the other I shot or from two shots.

Another type of manager. A sprat is given, for example, a coin is given three times. It is necessary to know the imovirnist of the fact that either all three times the coat of arms is vipade, or those who want the coat of arms to be vipade only once. Tse order for the zbіlshennya imovіrnosti.

A warehouse of insane podia

Addition of imovirnosti vikoristovuetsya only, if it is necessary to calculate the imovirnіst chi logical sum of vipadkovyh podіy.

Sumu podіy Aі B signify A + B or A ∪ B. The sum of two pods is called a pod, so it’s more or less the same, if you want one of the pods. Tse means what A + B- Podiya, as it is now, and even more so, if the hour of caution has become podiya A or else B, or at once Aі B.

Yakshcho podії Aі B mutually incomprehensible and yogo imovirnosti given, then imovirnist are those who, as a result of one trial, one of these podias will appear, redeem, vicorist, and fold the imovirnosti.

The folding theorem. The imaginativeness of what will be one of two mutually insane podias, more than the sum of the idioms of these podias:

For example, two shots were shot at the watering. Podia BUT- getting into pitching from the first post, hitting AT- Hit from another postil, podiya ( BUT+ AT) - I shot from the first or the other I shot or from two shots. Father, like two pods BUTі AT- nesum_snі podії, then BUT+ AT- Now I want one or two of them.

example 1. A box has 30 balls of the same size: 10 red, 5 blue and 15 white. Calculate the imovirnіst of what, do not be surprised, if you take a colorful (not white) ball.

Solution. It is accepted that BUT- “a red ball was taken”, and a podium AT- "the blue ball is taken." Todі podіya - "a colorful (not white) ball was taken." We know the imovirnіst podії BUT:

ta go AT:

Podії BUTі AT- It is mutually unimaginable that if one ball is taken, it is not possible to take balls of different colors. To that victorious fold of imitations:

The theorem of folding ambiguities for a number of insane pods. If you want to become impersonal, then the sum of their qualities is good 1:

The sum of the qualities of the proliferant pods is also 1:

Protilezhnі podії utvoryut impersonal podіy, and ymovіrnіst povnoї mnіzhini podіy dorіvnyuє 1.

Imovirnosti protilezhnyh podіy sound signify in small letters pі q. Zokrema,

why to use such formulas for the imovirnosti of the opposite subdivisions:

butt 2. The goal of the range is divided into 3 zones. The ability to shoot at the target in the first zone is 0.15, in the other zone - 0.23, in the third zone - 0.17. To know the imovirnіst of what the shooter can eat at the target and the imovirnіst of what the shooter can eat at the target.

Solution: We know the ability of what the arrows to eat with the target:

We know the imovirnіst of what the shooter can use to increase the goal:

The order of folding, in which it is necessary to zastosovuvat and add that plurality of qualities - on the side of the "Rizn_ of the order for the addition of that plurality of qualities" .

Storage of materials in mutually sleeping podiums

Two vipadkovі podії are called sleeping, as if the onset of one podії does not include the current other podії in that very guarded one. For example, when throwing a big brush, I will BUT I respect the vipadance of the number 4, but I AT- Vipadannya of the paired number. Oskіlki number 4 is a pair number, tsі dvі podії sumіsnі. In practice, there are plans for a rozrahunka of imitations to come alone from mutually sleeping pods.

The theorem of collapsing possibilities for sleeping pods. Imovirnist of the fact that one of the sleepy podias has come, the sum of the imovirnosti of these podias, for which the imovirnistnost of the solemn attack of both podias is seen, that is the tver of the ymovirnosti. The formula for the abilities of a sleeping person may look like this:

Oskіlki podії BUTі AT sums, sums BUT+ AT nastaє, yakscho nastaє one of the three possible podіy: otherwise AB. Appropriate to the theorem of folding insane sums, it can be calculated as follows:

Podia BUT come on, as if you are one of two insane podias: otherwise AB. However, the momentum of the present is one of the subdivisions of a number of insane ones, the most important are the sum of the imovirnosti of all of them:

Similarly:

Substituting virase (6) and (7) for virase (5), we take the formula of flexibility for double podia:

When varying the formula (8), follow the check that matches BUTі AT can buti:

• mutually independent;
• mutually dependent.

Imovirnosti formula for mutually independent subdivisions:

Equity formula for mutually dependent subdivisions:

Yakshcho podії BUTі AT insane, їх збіг є impossibly fluent i, such a rank, P(AB)=0.

Example 3. On auto hauls, when arriving on the first car, it is possible to win, when arriving on another car. Know:

• ymovіrnіst that scho pomozhut offending cars;
• the possibility of what one car can overcome;

1) Imovirnist of what the first car can overcome, do not fall short of the result of another car, to that BUT(we will overcome the first car) that AT(peremozhny friend's car) - independent podії. We know the ability to overcome offensive machines:

2) We know the possibility that we can overcome one of two cars:

The order of folding, in which it is necessary to zastosovuvat and add that plurality of qualities - on the side of the "Rizn_ of the order for the addition of that plurality of qualities" .

Verify the task of folding the assets on your own, and then look over the decision

Example 4. Fall two coins. Podia A- Removal of the coat of arms on the first coin. Podia B- The appearance of the coat of arms on another coin. Know the imovirnіst podії C = A + B .

Reproduction of Imovirnosti

Plenty of omnipotence vicorists, if the following count the imovirnіst logical dobutku podіy.

With any change of mood, you may be independent. Two podії are called mutually independent, as if the current one podії does not flow into the imovirnіst of the other podії.

The theorem of multiplication of possibilities for independent pods. Imovirnist of the one-hour advance of two independent pods BUTі AT dobutku ymovirnosti tsikh podіy and calculated for the following formula:

Example 5. Throw a coin three times later. Know ymovіrnіst, scho all three times vipade coat of arms.

Solution. Imovirnist of the fact that at the first throw of a coin the coat of arms was broken, suddenly, three times. We know the immovirnist that all three times vipade the coat of arms:

Verify the problem of multiple possibilities independently, and then look over the solution

Example 6.Є a box of nine new tennis balls. For a grill, take three balls, then put the grill back. When choosing balls, the faces of the non-faceted ones are not disturbed. What is the imovirnist of the fact that after three years the box does not run out of unbounded balls?

Example 7. 32 letters of the Russian alphabet are written on the cards of a pink alphabet. Five cards are drawn one by one and put on the table in the order they appear. Know the imovirnist of the fact that the word "kіnets" is from the letters.

Example 8. Three new decks of cards (52 leaves) are spun into the next chotiri cards. Know the imovirnіst of the fact that all tsі chotiri cards will be different suits.

Example 9. The same task, which is in the butt 8, but the skin card after the win is turned into a deck.

The task is more complicated, for some it is necessary to zastosovuvat and add that plurality of assets, as well as calculate the amount of money to be added - on the side of the "Responsibility for the addition of that multiplicity of assets."

Imovirnist of that, which will be seen if one of mutually independent podiums, can be counted by way of judgment for 1 additional immovability of adjacent podiums, then by the formula.