Probability is an important branch of mathematics, which studies random phenomena. In daily life, we often encounter some uncertain things, such as weather forecast, stock market fluctuation, game results and so on. These are random phenomena. Probability theory is to study the regularity of these random phenomena.
The basic concepts of probability theory are as follows:
1. random test: under the same conditions, tests that may produce different results and cannot determine the specific results before testing are called random tests. Such as coin toss and dice roll.
2. Sample space: The set of all possible results of random test is called sample space. For example, the sample space of coin toss is the reverse of the sign.
3. Random events: A subset of the sample space is called random events, which are usually represented by capital letters. For example, flipping a coin to get an avatar is a random event.
4. Probability: The numerical value describing the probability of random events is probability. The probability ranges from 0 to 1, including 0 and 1, indicating that the event cannot happen, and 1 indicates that the event will happen.
For the problem that "most people don't smoke", we can regard it as a random experiment, that is, a person is randomly selected from the whole crowd to see if he smokes. The whole is our sample space, and "smoking" and "no smoking" are two mutually exclusive random events. If we know the number and total number of non-smokers in the whole population, then we can calculate the probability of "non-smoking".
Probability theory has a wide range of applications in real life, such as evaluating the effectiveness of treatment methods in medical research, predicting the changes of stock prices in financial markets, and evaluating the reliability of systems in engineering fields. By quantitatively describing random phenomena, we can better understand and predict the world.
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Conditional probability is an important concept in probability theory, which describes the probability of another event when one event has already happened.