One of the basic concepts of tervers has already been stated above – it is an event. Events can be credible, impossible, or random.

A credible event is an event that, as a result of a test (the implementation of certain actions, a certain set of conditions) is bound to happen. For example, in terms of gravity, a coin tossed will certainly fall down.

An impossible event is an event that knowingly will not happen as a result of the test. An example of an impossible event: Under the conditions of terrestrial gravitation, a flipped coin will fly upwards.

Finally, an event is called random if, as a result of the test, it may or may not happen, and there must be a fundamental criterion of randomness: a random event is a consequence of random factors, the impact of which is impossible or extremely difficult to predict. Example: as a result of a coin toss an “eagle” will fall out. In the case considered, random factors are the shape and physical characteristics of the coin, the force/direction of the throw, air resistance, etc.

The underlined criterion of randomness is very important – so, for example, a card cheat can very cleverly imitate randomness and let the victim win, but we are not talking about any random factors affecting the final result.

Any result of a trial is called an outcome, which, in fact, is the occurrence of a certain event. In particular, when a coin is tossed, 2 outcomes (random events) are possible: heads will fall and tails will fall. Naturally, it is assumed that this test is conducted under such conditions that the coin cannot get on the edge or, say, hang in weightlessness.

Events (any) are denoted by capital Latin letters or by the same letters with subscripts, e.g.: . The exception is the letter , which is reserved for other needs.

Let us write down the following random events:

• A coin toss will result in an “eagle”;
• A roll of the die will result in 5 points;
• a card of the suit of clubs will be drawn from the deck (by default, the deck is full).

Yes, events are written in this way in practical problems, and it is convenient to use “talking” subscripts in appropriate cases (though one can do without them).

It should be emphasized for the third time that random events necessarily satisfy the above criterion of randomness. In this sense the 3rd example is again illustrative: if all cards of the clubs suit are initially removed from the deck, the event becomes impossible. On the contrary, if the tester knows that, for example, the queen of clubs lies at the bottom, he can make the event credible if he wants to =) Thus, this example assumes that the cards are well mixed and their shirts are indistinguishable, i.e., the deck is not mottled. And, here, “speck” doesn’t even mean “skillful hands” that eliminate the randomness of your winnings, but visible flaws in the cards. For example, the shirt of the queen of clubs can be dirty, torn, taped up with scotch tape… man, it’s some kind of manual for beginner chicatillos =)

Thus, when drawing an important lot it always makes sense to casually look to see if the faces of the coins are the same 😉

Another important characteristic of events is that they are equally possible. Two or more events are called equiprobable if none of them is more possible than the others. For example:

A roll of heads or tails on a coin toss;
1, 2, 3, 4, 5, or 6 on a die roll;
drawing a card of clubs, spades, diamonds or hearts from the deck.

This assumes that the coin and die are homogeneous and geometrically correct, and that the deck is well mixed and “perfect” in terms of the indistinguishability of the card shirts.

Can the same events not be equally possible? They can! For example, if a coin or die has its center of gravity displaced, then quite certain faces are much more likely to fall out. As they say, another loophole for cheaters. Events-extracting clubs, spades, hearts, or diamonds are also equiprobable. However, equiprobability is easily broken by a trickster who, while shuffling a deck (even a “perfect” one), will cleverly peek and hide in his sleeve, such as the ace of clubs. Here it becomes less possible that the opponent will be dealt a club, and more importantly, less possible that he will be dealt an ace.

Nevertheless, in the three cases considered, the loss of equal possibility still preserves the randomness of events.