What are the laws that classical probability conforms to, and what are the probability formulas of c

You made the mistake of conceptual confusion.

What is the law of distribution?

What is the distribution law for?

The distribution law is for random variables.

In the case of a discrete random variable, it is a series of formulas that represent the probability that the random variable will take all possible values.

And what is a classical probability problem?

Classical probability is relative to the outcome of an experiment, and the probability of each possible outcome of each random experiment is the same.

Here is the difference between experimental results and random variables.

Random variables are partial abstractions after observing the experimental results, and a certain characteristic of the experimental results is converted into numerical values for recording.

For example, in the classic coin toss experiment, the result is:

Let's say I have a coin with a 1 on the front and a 0 on the back

Then we can use x to represent the number shown by the experimental results.

There is x=1 when heads and x=0 when tails

In this case, since the probabilities of x=1 and x=0 are equal, they are evenly distributed.

This is just the simplest random variable.

Let's take a different example.

There are 4 weights in one box, 1g, 2g, 3g, 4g

Take out two at a time. Observations.

This is a classical probability problem. Because the probability of coming out of any two is the same. It is impossible for me to take 1G and 2G with a lower probability than with 3G and 4G.

But if we define a random variable, x is the total weight of the weights taken out.

Then it's clear that it's not that simple.

Because note: taking out 1g and 4g (x=5) and 2g, 3g (x=5) will make x=5, so the probability of x=5 is higher than that of other 3g, 4g 6g and 7g, so the random variable x does not obey a uniform distribution, because all the possible probabilities of its value are not the same. But this experiment is still a classical probability problem, taking out 2g, 3g and 1g, 4g are different results, we define x, their x is the same, not they are the same in themselves.

Other normal distributions (this is a distribution characteristic of continuous random variables, not marginal to classical probability).

Poisson distribution, uniform distribution is the distribution law of a random variable in a certain experiment (note, not necessarily classical probability).

6. The word lottery is not enough to explain an experimental process.

Exactly how to do the experiment. For example, if I say that I toss a coin, I can make two tosses and n observations of possible results, just talking about lottery tickets, and it is impossible to say that it conforms to a certain law without setting a suitable random variable for the result.

I studied mathematics and only finished probability theory last semester. But I don't particularly understand your question, so I'll give you a rough idea.

There are two requirements for the classical generalization that we are talking about in class.

All outcomes of the trial are limited and the probability of each outcome occurring is equal.

But uniformly distributed, normal, Poisson, these are all continuous, which means that the results of the experiment are generally within a range, not a finite.

In general, if an event A represents a small region in a region S, then the probability of A occurring is the area of A divided by the area of S (it can also be another measure, such as length, volume, etc.), this probability is called geometric probability, and its sample points are uniformly distributed within S.

But I don't know how normal and Poisson distributions have anything to do with classical probability.

I haven't bought a lottery ticket, and I don't know what the specific rules are, so it's hard to say. If it is similar to **, for example, there are a total of 1 million, but only one can be won, and everyone is randomly drawn, then this is also a classical generalization, because the probability of each person drawing is 1 in 1 million, and the result of each person's lottery is limited: winning or not winning.

Some personal understanding may not actually help your problem.

Oh, I guess you are a lottery enthusiast and want to find some basis from probability theory.

Probability and distribution, Mo Wen ghost animal has been explained.

Let's talk about the lottery that LZ might care about, assuming that the lottery design is as follows: 30 numbers draw 1 number. Then the results of a randomized trial are not possible, but there are 30 possible outcomes, and the probability of each outcome is 1 30.

Then this lottery experiment belongs to a classical generalization.

Moreover, the specific correlation it reflects is also a classical generalization.

For example, if we extract enough numbers of 30 numbers with the same probability of the same result from the two tests, then the number of times that 1 30 numbers have the same result from the two tests tends to be equal, that is, the probability is uniform.

Another example: the nth and nth 1st times the result is the same (counted as a) the nth and nth times the result of the test is the same (counted as b) If we extract enough times, then the limit of a b is 1, that is, the probability of occurrence is equal.

That is, if you arbitrarily design some kind of uniform correlation about the probability of occurrence of 30 numbers (rather than an uneven association, such as the sum of the previous and late periods, and the sum of any two numbers is uneven), then when you observe the experimental results of this correlation are also uniform, which means that the probability of their occurrence is actually equal.

Applause Mo asked the ghost animal to say it so well, it was completely to the point.

The problem is this, the poisson distribution is normal, the exponential distribution is exponential. It's all about random variables, and if you learn about random processes, you will understand.

Probability and distribution are different concepts and cannot be compared in this way.

Classical probability is more difficult in probability, permutations and combinations are used more, our teacher said, when you go to college, don't study the baffle method in permutations and combinations, because probability theory uses the knowledge of advanced mathematics to study probability. The 1234678 you ask is pointless.

I'm a college student and I'm studying probability theory right now;

To determine whether a classical probability problem is a problem, two conditions must first be met:

1. There are only a limited number of sample points in the sample space of the experiment.

2. The occurrence of each basic event in the test is equally possible.

The number of lottery tickets meets the first point, and it is limited;

The lottery ticket you buy is any one of all the lottery tickets, before you buy it, the probability of any lottery ticket being bought by you is equal, but because there are too few prizes, and there are too many lottery tickets, then divide the total number of winning tickets by the total number of lottery tickets is your probability of winning, of course, it is very small!

A little bit unsure of your purpose in asking this question?

It feels like a dead definition, and such a distinction is meaningless.

I just had it in college textbooks, I didn't care, and it was useless.

It is inherently problematic to say that the equal probability probability corresponds to what division, and many divisions can be considered a combination of equal possible divisions from one side).

Probability originated in the middle of the seventeenth century, when a large amount of random data needed to be sorted out and studied in the fields of error analysis and demographics, thus giving birth to a kind of mathematics that specialized in the study of the regularity of random phenomena. See for details.

Your question is wrong, "I can go and ask the probability math teacher."

Classical generalizations, also called traditional probabilities, were defined by the French mathematician Laplace.

Proposed. If a randomized trial contains a finite number of unit events, and each unit of event has an equal probability of occurring, then the randomized trial is called the Laplace test, and the probability model under this condition is called the classical generalization.

Under this model, all possible outcomes of a random experiment are limited, and the probability of each basic outcome occurring is the same. Classical generalizations are probability theory.

The most intuitive and simple model, many of the rules of probability, were first derived from this model.

Examples of classical generalizations:

Toss a coin with a uniform texture and a well-shaped shape, and the probability of both heads and tails is the same, both are 1 2. The coin is uniform in texture and has a standardized shape, neither side has more chances of appearing than the other, and the probability of both heads and tails appearing is the same. This is called the symmetry of classical generalizations, and sports competitions often use this law to determine who kicks off, and who chooses the venue.

In order to explain this phenomenon, in history, many masters have verified this problem, and it can be seen that with the increasing number of times, the frequency of positive appearances is getting closer and closer to 50%, and we also have reason to believe that as the number of times continues to increase, the frequency of positive and negative appearances will be fixed at 1 2, that is, the probability of positive and negative occurrences is 1 2.

Classical probability formula: c (subscript n, superscript m) = n!/（m! *n-m）!）c34=4x3x2x1/3x2x1=4

c36=6×5×4/3×2×1=20

c12=2x1/1=2

Classical probability, also known as ex-ante probability, refers to the timing of a random event.

The probabilities of the various possible pre-swim outcomes and the number of occurrences of them can be known by deduction or extrapolation, without any statistical experiments.

Classical Definition of Probability:

If a trial satisfies both :

1) Trials have only a limited number of basic results.

2) The likelihood of each basic outcome of the trial is the same. Such an experiment is a classical test.

For event a in a classical trial, its probability is defined as: p(a) = m of n, where n is the total number of all possible basic outcomes in that trial. m represents the number of baseline results of the trial included in event a.

This method of defining probability is called the classical definition of probability.

Probability is a numerical measure of the likelihood of a chance event occurring. Suppose after many repeated experiments (represented by x) and several times by chance (represented by a) occur several times (represented by y).

With x as the denominator and y as the numerator, a numerical value (represented by p) is formed. In multiple experiments, p is relatively stable at a certain value, and p is called the probability of a occurrence. If the probability of a chance event is determined by long-term observation or a large number of repeated experiments, then such probability is statistical or empirical.

The discipline that studies the internal laws that govern accidental events is called probability theory. It belongs to a branch of mathematics. Probability theory reveals the manifestations of the internal laws contained in accidental phenomena.

Therefore, probability plays an important role in people's understanding of natural and social phenomena. For example, the amount of social goods that need to be deducted before they are distributed to individual consumption, and the proportion of accumulation that should be accounted for in national income need to be determined using probability theory.

Definition of classical probability: If the number of possible basic events in an experiment is n, and event a contains the number of basic events m, the probability of a.

Classical probability, also known as ex-ante probability, refers to the fact that when the various possible outcomes in a random event and the number of occurrences can be known by deduction or extrapolation, the probability of various possible outcomes can be calculated without any statistical experiments.

A classical definition of probability

The probability formula for classical generalizations is p(a)=mn=a, the number of basic events contained in a, the total number of basic events, n.

If there are n possible outcomes in an experiment, and all outcomes are equally likely, then the probability of each fundamental event is 1 n; If an event A contains m outcomes, then the probability of event A is p(a) = m n = the number of basic events that a contains m the total number of basic events n.

Summary. Classical probability, also known as ex-ante probability, refers to the fact that when the various possible outcomes in a random event and the number of occurrences can be known by deduction or extrapolation, the probability of various possible outcomes can be calculated without any statistical experiments.

Example of conditional probability: This is the probability of event A occurring under the condition that another event B has already occurred. The conditional probability is expressed as p(a|b), read as "probability of a under condition b".

Teacher, I would like to ask how to distinguish between conditional and classical probabilities.

Classical probability, also known as ex-ante probability, refers to the fact that when all possible outcomes and the number of occurrences of random events can be known by deduction or extrapolation, the probability of various possible outcomes can be calculated without any statistical experiments. Conditional probability example: This is the probability of event A occurring under the condition that another event B has already occurred.

The conditional probability is expressed as p(a|b), read as "probability of a under condition b".

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