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Laws casual

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All our life probability laws correct. Who knows, what waits for us tomorrow - a prize in a lottery or accident? Precisely to predict the future it is impossible. But, possessing the necessary information, it is possible to count degree of probability of this or that event.

Throwing a coin, we say that probability of loss "юЁыр" or "Ёх°ъш" makes 50 on 50. It means that from 100 attempts the coin will lay down 50 times "юЁыюь" upwards and as much - "Ёх°ъющ". However, to speak about probability 50:50 it is not absolutely true, as the chance or probability of the given event is a number proisshedshih the events, divided into total number of the received results. Thus, and "юЁхы" and "Ёх°ър" can drop out on 50 times from 100. It is possible to express probability degree as 50%, 0.5, 1 of 2 or 1/2.


Chances

Sometimes instead of probability of event we speak about chances for or against, correlating number of chances in advantage and against the given event. In a case with one coin from two possible results there is one chance that "юЁхы" will drop out, and one - that will not drop out. Therefore their parity makes 1:1, or chances are equal. Saying that there are only two possible variants of falling of the thrown coin, we reject insignificant probability of falling of a coin on an edge. However at calculation of chances it has no value - this result prenebregut and will throw a coin once again. Now we will try to throw at once two coins. Will drop out as a result or two "юЁыр" or two "Ёх°ъш" or "юЁхы" and "Ёх°ър". It would Seem, the chance of each of these results is equal 1/3. However, having thrown two coins of 100 consecutive times, you will find out that two "юЁыр" and two "Ёх°ъш" have dropped out approximately on 25 times, and a combination of one "юЁыр" with one "Ёх°ъющ" - nearby 50. Means, chances for two "юЁыют" and two "Ёх°хъ" make approximately on 1/4, but for one "юЁыр" and one "Ёх°ъш" - nearby 50/100 or 1/2. Why so it turns out?

The Answer is easy for finding if to take one copper and one silver coin. A combination "юЁхы-Ёх°ър" can drop out in two ways: or copper "юЁхы" and silver "Ёх°ър" or on the contrary. Differently, possible results here not 3, but 4. Two of them give a combination "юЁыр" and "Ёх°ъш" and only on one - two "юЁыр" and two "Ёх°ъш". That is why combinations "юЁхы-Ёх°ър" drop out twice more often, than any another. In this case chances against two "юЁыют" make 2:1 and as much against two "Ёх°хъ" whereas at a combination "юЁхы-Ёх°ър" chances 1:1.


Shifts

In a case with two coins of mathematics would tell that there are four possible shifts "юЁыр" and "Ёх°ъш" but only in three possible combinations. Differently, shift "юЁхы-Ёх°ър" it is not identical to shift "Ёх°ър-юЁхы" but both make one combination. Here it is easy to get confused, as in an everyday life these words are applied in other value. The digital lock, opening a combination 1-2-3-4, will not open if to type 1-3-2-4. Being one mathematical combination, both sets of figures are different shifts. So more correctly to name this lock "яхЁхё=рэютюёэ№ь". Also incorrectly name permutatsiej, or "яхЁь" a combination of figures on the football coupon.

Total number of the shifts received at podbrasyvanii of coins, it is possible to calculate, having multiplied quantities of variants of falling of each coin. Having two coins, we will receive 2x2=4 shifts. With 4 coins it will turn out 2 h 2 h 2 h 2=16 shifts.

In the Same way it is possible to count number of shifts for playing bones. We will tell, for two bones their number is equal 6 h 6=36, and for three-6x6x6=216.

What chance of what at two first comers the person birthdays will coincide? If to neglect in the superfluous days of leap years then it is equal 1/365. In other words, it is rather improbable. If to take a class from 36 pupils, it is possible to think that the chance of such coincidence is still insignificant - approximately 36 of 365 or 1/10. But, as it is surprising, actually it it is ready above - 8:10 or 80%.

Brilliance.

Unique difficulty in such problems is the great number of possible shifts. Birthday can coincide at John and Mary, at Mary and Freda or at any other pair of pupils. And in a class from 36 children there are 630 possible steams. The matter is that there are 36 variants of a choice of the first member of pair and 35 - the second. Having multiplied 36 on 35, we will receive 1260 shifts, but number of combinations twice less than this figure, as, for example, shifts "-цюэ-¦ІЁш" and "¦ІЁш--цюэ" are one combination. Therefore total number of combinations equally 1260/2=630. Fortunately, instead of considering all these variants, our problem can be solved easier. We will consider a variant of full discrepancy of birthdays.

If we ask all pupils to name by turns the birthday 364 chances from 365 or 364/365 will be that the second of the named days will not coincide with the first. The chance of discrepancy of the third of the named days with first two makes 363 of 365 as already two dates from 365 now can coincide. Having continued up to the end, you will find out that the chance of discrepancy of Zb Th under the account of birthday with the others is equal 330/365 or about 90%. However, the chance of full discrepancy of birthdays in a class can be calculated, having multiplied all these fractional sizes. Try to make it on the calculator and will see that the chance of full discrepancy of days of births is equal approximately 20%.


And what on the average?

When we say about pjatidesjatiprotsentnoj probabilities of that something will occur, we mean that this event occurs on the average in 50 cases from 100. But results even several simple experiences can suggest otherwise. We take an extreme case. Having thrown a coin of all once, we will receive or absolute "юЁыр" or absolute "Ёх°ъѕ". But, throwing a coin many time, we will see that percent "юЁыют" comes nearer to fifty. Someone wrongly believes that this fact helps to expect the events depending exclusively from will of a case. We will tell, if "юЁхы" has dropped out four consecutive times once again the coin, most likely, will fall "Ёх°ъющ" upwards. The reason ostensibly that for the sake of preservation gold pjatidesjatiprotsentnoj the middle "Ёх°ър" it is simply necessary. Actually in long to a number of events hardly there will be such point, where a parity "юЁыют" and "Ёх°хъ" Would equal precisely to fifty percent, and it is a question only of figure round which it will fluctuate. But between settlement and actual quantity "юЁыют" and "Ёх°хъ" usually always there is a small divergence. For example, four superfluous "юЁыр" among from 1000 podbrasyvany (502 "юЁыр" 498 "Ёх°хъ") will yield result very close to fifty percent prognosticheskih "юЁыют" which will be considered as acknowledgement of calculations. Corrected that the result of one casual event of this kind does not influence result of the following. Such events name independent.

Not all events are independent. For example, the chance to extend a card of red colour from a usual pack in 52 sheets is equal to fifty percent. However after that in your pack there will be 25 red cards from 51. Therefore the chance to extend the following red card will make now 25/51 or about forty nine percent. Certainly, if the taken out card each time to return in a pack the chance will always extend a card of any colour it is equal to fifty percent. In some gamblings skilled players can constantly win, is tenacious keeping in the memory the dumped cards and estimating chances of occurrence in them or at partners of the cards necessary to them.


Handbook men

Handbook men In gamblings for the sake of a profit or pleasure are staked on certain result or event. Not in forces to struggle with a temptation, some people prosazhivajut behind a gambling table fabulous money. To Someone, the truth, is possible to break a large sum, but the majority, finally, remains in loss. That is why in a gaming separate people, and the whole companies for the sake of the profit arriving from clients trade. Handbook men on jumps get profit, offering on participants of arrival of the rate more low (or above) the actual. We will tell, if six participate in running absolutely equal on forces of hounds of dogs, chances of each of them of a victory are equal 1/6. Therefore the correct rate on each dog should be 5:1. But the handbook man offers only 4:1. It means that put on the winner will receive back the money plus four times more. If each of six players puts 100 pounds on the dog, the handbook man will receive 600 pounds. Whatever of them has won, it will pay only 500 pounds, i.e. 100 pounds of the rate plus 400 more, having left in a pocket superfluous one hundred.


Game for gawks

In practice the handbook man changes rates depending on the sum of the put money. Rates on the recognised favourite will gradually decrease to reduce payments in case of its victory. At the same time rates on notorious "ёырсръют" will raise to urge on players. Finally, the handbook man wins, and players remain in loss.

At the beginning the British national lottery was exposed to the severe criticism because of absolutely insignificant chances to win the main prize - approximately 14 million to one. However its success was promoted in many respects by size of the main prize and that fact that the considerable part of the money brought for tickets, goes on the charitable purposes.


Insurance

Many people declare that they is resolute against any gamblings. Nevertheless, each of us plays with destiny after the own fashion. Even street transition is interfaced to known risk as pedestrians sometimes perish under wheels of motor vehicles. However it is possible to soften accident consequences, having bought an insurance policy. The insurance is some kind of a bet which we hope to lose. Differently, we argue with the insurance company that we will get to any trouble. If and happens, we win a bet, and the company pays indemnification to us or the close relative in case of our death. The insurance company as the real handbook man, gets profit, paying under the insurance less, than it has been collected for the sold policies.