How many times can you try to open all the locks at most? The keyword "most" should actually be calculated as follows: there are five keys at the beginning, and at most the last key can be matched with the lock. Then you only need to try three times when there are four left, twice when there are three left, and 1 time when there are two left, which adds up to 4+3+.
Extended data:
Basic knowledge of probability of college entrance examination mathematics problems
Independent events are completed by multiplication, that is, the result of the second time is not affected by the first time;
Mutually exclusive events did it by addition, that is, the first thing happened and the second thing didn't happen.
Probability is essentially a matter of two counting principles.
There are different ways to accomplish one thing, and each way has different methods. In this way, all methods to accomplish this must add up the methods in each method. (addition principle)
If there are different steps to accomplish one thing, then each step has different methods. In this way, all the methods to accomplish this must be multiplied by all the methods in the step. (principle of multiplication)
Mathematical probability statistics of college entrance examination
Discrete random variable distribution table
1. Random variables and related concepts
① The result of random test can be expressed by a variable, called random variable, which is commonly expressed by Greek letters ξ, η, etc.
② The possible values of random variables can be listed in a certain order. This kind of random variable is called discrete random variable.
③ Random variables can take all values in a certain interval, and such random variables are called continuous random variables.
2. Discrete random variable distribution table.
① The concept and properties of discrete random variable distribution table.
4. Sampling method and estimation of population distribution
sampling method
1. Simple random sampling: let the number of a population be n, and if a sample is extracted from it one by one, and the probability of each individual being extracted is equal each time, it is called simple random sampling. Commonly used are lottery method and random number table method.
2. Systematic sampling: When there are a large number of people in the group, the group can be divided into several balanced parts, and then 1 individual can be extracted from each part according to predetermined rules to get the required samples. This kind of sampling is called systematic sampling (also called mechanical sampling).
3. Stratified sampling: When the known population consists of several parts with obvious differences, it is often divided into several parts first, and then sampled according to the proportion of each part. This kind of sampling is called stratified sampling.
Sample estimation of population distribution
Because the population distribution is usually difficult to know, we often use the frequency distribution of samples to estimate the population distribution. Generally speaking, the larger the sample size, the more accurate this estimation is.
Population distribution: the probability distribution law of population value is usually called population distribution.
When individuals in a group take several different values, their frequency distribution table is represented by different values and corresponding frequencies in the sample book, and the geometric representation is the corresponding bar chart.
When the individual values in the population are within a certain range, the frequency distribution of the corresponding samples is represented by the frequency distribution histogram.
Overall density curve: when the sample size increases infinitely and the grouping distance decreases infinitely, the histogram of frequency distribution will approach a smooth curve infinitely, that is, the overall density curve.