A, b and c are independent of each other if:

P(AB) = P(A) P(B)

P(BC) = P(B) P(C)

P(CA) = P(C) P(A)

P(ABC) = P(A) P(B) P(C)

One * * * four conditions, each of which is essential.

If there is only the last condition, there are counterexamples on the Internet, as shown below:

Extended data:

Probability theory is a branch of mathematics that studies the quantitative laws of random phenomena. Random phenomena are relative to decisive phenomena. The phenomenon that a certain result must occur under certain conditions is called decisive phenomenon. For example, at standard atmospheric pressure, when pure water is heated to 100℃, water will inevitably boil.

Random phenomenon means that under the same basic conditions, before each experiment or observation, it is uncertain what kind of results will appear, showing contingency.

For example, when you flip a coin, there may be heads or tails. The realization and observation of random phenomena are called random experiments. Every possible result of random test is called a basic event, and a basic event or a group of basic events is collectively called a random event, or simply called an event. Typical random experiments include dice, coins, playing cards and roulette.

The probability of an event is a measure of the possibility of an event. Although the occurrence of an event in random trials is accidental, those random trials that can be repeated in large numbers under the same conditions often show obvious quantitative laws.

Events include unit events, event space, random events, etc.

The only and independent result that may occur in a random experiment is called a unit event, which is represented by E, and the set of all possible unit events in a random experiment is called an event space, which is represented by S. For example, in a random dice test, if a unit event is represented by the number of points obtained, there may be six unit events in a * * *, and the event space can be represented by S={ 1, 2, 3, 4, 5. ?

The event space above is composed of countable finite unit events. In fact, there is also an event space composed of countable infinite and uncountable unit events. For example, in a random coin toss test until the national emblem is obtained, the event space consists of countless unit events, which are expressed as: S={ country, several countries, counting countries, ...}. Note that in this example,

When two chopsticks are thrown at the table at will, the intersection angle formed after being stationary is assumed to be α, and the composition of the event space of this random experiment can be expressed as.

A random event is a subset of the event space S, which is composed of unit elements in the event space S, and is represented by capital letters A, B, C ... For example, in a random test of two dice, let random event A= "the sum of points obtained is greater than 10", then A can be composed of the following three unit events: A = {(5,6), (6,5).

If in a random experiment, all possible unit events occur in the event space, this event is called an inevitable event, which is expressed as; Accordingly, if the event space does not contain any unit events, it is called an impossible event, which is expressed as.

References:

Baidu encyclopedia-probability theory