For practice it is very important to be able to estimate degree of uncertainty of the most various experiences in number. Let's begin with consideration of the experiences having to equiprobable outcomes. It is obvious that degree of uncertainty of each such experience is defined by number to: if at k=1 the experience outcome is not casual at all, at big to predict an experience outcome very much and very difficult. Thus, required numerical degree of uncertainty has to be function of number to, at to =1 to address in zero and to increase at increase of number to.
There are 25 coins of one advantage; 24 from them have identical weight, and one – false – some easier other. It is asked, how many weighings on cup scales without weights it is possible to find this false coin.
specifies as far as implementation of experience of B reduces uncertainty And. This difference designate amount of information concerning experience And, the B containing in experience, or, well, information about And, containing in B. Thus, we have an opportunity of numerical change of information.
I think, it is excessive to say that the theory of information has huge value for development of modern science and equipment. It was widely used in physics, microelectronics, and also in all branches of equipment where it is necessary to solve problems of storage, receiving and information transfers.
Let's notice that after two weighings we still have to have no more than three possible outcomes of experience And. From this it follows that the number of the doubtful coins which are not participating in the second weighing should not surpass
0 ≤ p (A) ≤ 1, log p (A) cannot be positive, and – p (A) of log p (A) – negative ( (– probability of receiving an outcome And in experience. Also we will notice that if it is not enough, and work – p (A) of log p (A) too will be very small, though positive, i.e. at work – p log p beyond all bounds decreases. Entropy of experience is equal to zero when one of its outcomes have degree of probability 1, and the others – probability degree the Greatest entropy has experience with equiprobable outcomes.
The main property of casual events is the absence of full confidence in their approach creating known uncertainty when performing of the experiences connected with these events. However it is absolutely clear that degree of this uncertainty in various cases will be absolutely different. Emergence of the mathematical theory of information became possible after was conscious that the amount of information can be set number.
Can often happen that, wishing to learn an outcome of any experience And, we can choose for this purpose differently experiences B. In this case it is always recommended to begin with that experience of B0 which contains the greatest information relatively And as at other experience of B we will possibly achieve less considerable reduction of degree of uncertainty And. Really, of course, it can turn out and vice versa.
The general uncertainty of the experience having to outcomes is equal to the sum of the brought by each outcome. This number is called entropy of experience And, we will designate it through N (. Let's consider some properties of entropy. First of all, it cannot accept negative values: since always