The formula of probability c is: C(n, k) = n (n-1) (n-2) (n-k+1)/k! , where k ≤ n. For example, c (12,3) =12×110/3! = 1320/(3×2× 1)= 1320/6=220。
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Probability, also known as "probability", reflects the probability of random events. Random events refer to events that may or may not occur under the same conditions. For example, it is a random event to randomly select one from a batch of goods with genuine products and defective products, and "what is extracted is genuine products". Suppose a random phenomenon is observed n times, in which event A appears m times, that is, its frequency is m/n.
The phenomena observed in nature and society can be divided into deterministic phenomena and stochastic phenomena. Probability is a branch of mathematics that studies the quantitative laws of random phenomena. On the one hand, it has its own unique ideas and methods. On the other hand, it is closely related to other branches of mathematics and is an important part of modern mathematics.
Probability is widely used in almost all fields of science and technology, such as weather forecast, earthquake forecast and product sampling survey. All sectors of industrial and agricultural production and national economy can be used to improve the anti-interference and resolution of signals in communication engineering.
What is the probability of two heads when you flip a coin twice? According to the knowledge of probability theory, it should be multiplied by two halves, that is, a quarter. If you count directly, there are four possible results when you flip a coin twice: heads, tails, and tails anyway. The probability of each result is the same, so the probability of two heads is one in four.
This example is given to illustrate that if you want to do something in several steps, each step has several possibilities, then the possibility of the final result is equal to the product of the probabilities of each step. For example, if you flip a coin twice, the probability of the first head is half, and the probability of the second head is half, then the probability of a positive result is one in four. This law is called multiplication principle in probability.
How to apply the principle of multiplication in practice? Arrange three groups of numbers from L to 10. The probability of finding a specific number in each group is one tenth, so the probability of guessing all three positions by choosing a number is 0.1* 0.1* 0.1= 0.001. If you guess a single and double combination, such as a single and double combination,
The probability of three groups appearing is 0.27, so what is the probability of three groups appearing twice in a row? 0.27*0.27=0.0729, which is about 7%.