Probability theory classical, the classical definition of probability

All three digits consisting of the numbers 0, 1, 2, 3, 4, 5 and each number appearing at most once.

There are 100 of them.

6*5*4=120, minus 5*4=20 starting with 0, 120-20=100).

1) Find the probability that the number is odd.

If the number is odd, then the last digit can only be 3, or 5

When the last digit is 3, there are 5 choices for the first and second digits (0, 1, 2, 4, 5) to choose two from the 5, and in order, there are 5*4=20 ways.

Except for those that start with 0, there are 4 types, and there are 16 types left.

In the same way, there are 16 types ending in 5.

So the last digit is 3 or 5, and there are 16 + 16 = 32 in total.

The probability is 32 100=

2) Find the probability that the number is greater than 330.

The number is greater than 330

Method 1, start with 5.

There are 5*4=20 such numbers. (It's a 5 selected, and the remaining 01234 picks two of them, in order).

Method 2, start with 4.

There are also 20 such numbers, for the same reasons as above.

Method three, start with 3.

At this time, the second digit must be 4 or 5

When the second digit is 4, it is 34?

At this time, it is to pick one of the remaining 0125 to be the third place, and there are 4 options.

When the second digit is 5, it is 35?

At this time, it is to pick one of the remaining 0124 to be the third place, and there are also 4 options.

So, there are a total of 8 options for numbers starting with 3.

Therefore, there are 20 + 20 + 8 = 48 kinds of numbers greater than 330.

The probability is 48 100=

There are 100 total three digits composed of the numbers 0, 1, 2, 3, 4, 5 and each digit appears at most once, i.e. 5*5*4=100

1) 3*4*4=48 single digits are odd numbers, the probability is 3, the hundred digits are not 0, then there are 4 selectable numbers, and the ten digits are the remaining 4, that is, 3*4*4=48 48 100=

2) 2) 2 + 1 * 5 * 4 = 34 requirements greater than 330, then when the hundred is 3, the ten can only be 4 and 5, four kinds of hundreds, that is, 1*2*4; When the hundred digit is 4, there are 5 kinds of single digits, and there are 4 kinds of tens, that is, 1*4*4; When the hundred digit is 5, there are 5 kinds of single digits, and there are 4 kinds of tens, that is, 1*5*4

Finally, add 1*2*4+1*5*4+1*5*4=48 48 100=

1) The number of three-digit numbers is 5*5*4=100

The odd number is 3*2*4+2*3*4=48, then the probability is 48 100=48%.

2) If the number is greater than 330, it is 2*5*4+2*4=48, then the probability is 48 100=48%.

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.

The classical definition of probability is classical probability.

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.

Classical probability is based on the assumption that the events that can occur with random phenomena are finite and incompatible, and that each fundamental event is equally likely.

For example, tossing a straight coin, heads and tails are the only two basic events that can occur and are incompatible with each other. If the occurrence of a positive event is denoted as e, and the probability of occurrence of an event e is denoted as p(e), then:

p（e）=1/（1+1）=1/2

Generally speaking, if there are a basic events that constitute event a and b events that do not constitute event a within the range of all possible basic events, then the probability of event a occurring is:

p（a）=a/（a+b）

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 approximate pre-probability of various possible outcomes when various possible outcomes in a random event and the number of occurrences can be known by deduction or extrapolation, without going through any statistical experiments.

The probability formulas for classical generalizations are described as follows:

p（a）=n（a）/n（s）。

Classical generalizations are the most fundamental and important concepts in probability. It defines the basic theories of probability, presents many interesting hypotheses and conclusions, and also serves the development of mathematics and computer science. In short, classical generalization is a method of calculating probability by observing whether an event occurs or not, that is, the conditional probability of an event occurring under certain conditions, which is expressed in mathematical form as a classical probability formula.

The probability formula for classical generalizations is: p(a)=n(a) n(s), where p is the probability, a is the event, s is the experimental space, and n(a) n(s) is the probability of the event. where n(a) is the number of outcomes satisfying condition a, and n(s) is the total number of outcomes satisfying condition s.

The basic concept of the probability formula of the classical generalization is that if the experiment is carried out n times, where event a occurs m times, then the probability of event a occurring is equal to m divided by n: p (a) = m n.

Ancient probability formulas are relatively simple, but they contain rich mathematical connotations. Within the framework of the distribution theorem, the basic principles of probability theory, the probability formulas of classical generalizations can be used to calculate the expected value, variance, and relationship between the occurrence of an event in an experimental space. The classical generalized probability formula also provides a basis for the theoretical development of correlation probability based on classical generalizations, forming a complete theoretical system of probability, which provides a basis for the research of the emerging branches of probability.

The classical generalization formula also provides reference and guidance for other scientific fields, especially in computer technology and information processing. Classical generalized probability formulas can be used to establish reasonable evaluation models to estimate the likelihood of an event occurring, and can also be used to estimate the reliability of the individual components in the system and the credibility of the individual system models. The results of these estimates can be used to measure the performance of the analytical system, based on which a more efficient, stable, and reliable system can be designed.

In addition, the probability formulas of classical generalizations can be applied to more fields, such as statistics, financial chiropractic, decision theory, operations research, social science, etc. In these areas, classical probabilities are often used to study uncertain risks and outcomes to make informed decisions and help make the best decisions.

In short, the probability formulas of classical generalizations and the probabilistic theories they cover are the basis of all current probability studies. It helps to better understand the trends of uncertain events and provides guidance for more informed decision-making. Probability formulas of classical generalizations can also be used in many fields, from mathematical modeling to computer technology, and have become an important theoretical and tool support for probability and related fields.