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How to calculate the probability theory in the lottery

How to calculate the probability theory in the lottery

Participation in the lottery - it's a way to test your luck, intuition and, if lucky, to break the bank, won a substantial amount.

In principle, almost any lottery can be analyzed from the point of view of the theory of probability, which will calculate the odds of winning.

Theory and terminology

set of lotteries is carried out continuously in the world withvariety of rules, victory conditions, prizes, but there are general principles for calculating the probability of winning, that can be adapted to the conditions of a particular lottery. But first, it is desirable to define the terminology.
Thus, the probability - is the calculated scorethe possibility that a given event will occur, which is often expressed in the form of the desired ratio of the number of events to the total number of outcomes. For example, the probability of "heads" when tossing a coin - one to two.
Accordingly, it is obvious that the probabilityWin - is the ratio of the number of winning combinations for all possible. However, we must not forget that the criteria and the definition of 'win' may also be different. For example, in most uses such definition lotteries as "winning class." to the requirements of the third class win less than to win the first, so the probability of winning the first class is the lowest. As a rule, such a prize is the jackpot.
Another significant moment in the calculations isthat the probability of two related events is calculated by multiplying the probabilities of each of them. Simply put, if you toss a coin twice, the probability of "heads" every time will be equal to one to two, but the chance that the "Eagle" will fall both times, will be only one in four. In the case of the three tosses a chance at all to drop to one to eight.

Calculating odds

Thus, the chance to calculate the payoffjackpot lottery in the abstract, where you have to correctly guess the number of dropped values ​​of a certain number of balls (for example, 6 out of 36), you need to calculate the probability of each of the six balls and multiply them together. Note that a decrease in the number of balls left in the drum, the probability of getting the right ball change. When first ball likelihood that the desired fall is 6 to 36, that is, 1 to 6, the second chance is 5 to 35 and so on. In this example, the probability that the ticket would be advantageous to 6x5x4x3x2x1 36x35x34x33x32x31, ie 720 to 1402410240, which is equal to 1 to 1,947,792.
Despite such frightening numbers people regularlywins the lottery worldwide. Do not forget that even if you do not take the main prize, there are also gains the second and third classes, the probability of getting that much higher. In addition, it is clear that the best strategy is to buy more tickets of the circulation, as each additional multiple of the ticket increases your chances. For example, if you buy more than one ticket, but two, and the probability of winning will be twice as much, two of 1.95 million, which is about 1 to 950 thousand.

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