Probability problems are very common in our public exams. It reflects the probability of random events, and usually likes to combine with permutation and combination to examine everyone. Having studied the probability problem in mathematics, we all know the probability of asking one thing to happen. We can use this formula: the probability of an event P= the number of situations that meet the conditions? The total number of situations, to calculate the required probability, but there is often a kind of problem in the topic, and the probability of solving it positively will be relatively complicated, such as a simple coin toss example:

For example: What is the probability of three consecutive coin flips, at least one of which is one-on-one?

Analysis: At least one time it is positive, which means it may be 1 time, 2 times and 3 times. It is relatively complicated to discuss each situation separately. If we put it another way, the opposite situation of facing up at least once is that it is back all three times, then the probability of being back all three times can be found in one step, and the total probability is 1. The reserve probability minus the total probability is the required probability, and we can get that the probability of at least one face up is 7/8.

Through this small example, we can easily find that when the situation of positive thinking is complicated, we can try reverse thinking, which saves time and is not easy to make mistakes.

Summarize a formula for everyone: positive probability = 1- negative probability, which is suitable for the complicated positive consideration in probability problems. Look at some real questions:

(Zhejiang in 2020) A company selected 10 innovative projects, and selected the best three projects to put into operation. Xiao Zhang made a random prediction and chose three projects. Ask him which of the following intervals is the probability of guessing at least 1 selected project?

A. Less than 50%

B.50%~60%

C.60%~70%

D. Over 70%

The first step analysis, this question examines the probability problem, belonging to the basic probability class.

Step 2: What is the probability of guessing at least 1 multiple choice questions? The front is difficult to solve, and the back is difficult to solve. At least the probability of guessing 1 =1-the probability of all wrong guesses. The total number of cases is three randomly selected from 10, the number of cases is, the number of cases is three randomly selected from the wrong seven, the number of cases is, the probability of completely guessing is, so the probability of guessing at least one is.

Therefore, choose the d option.

(Zhejiang, 202 1) The researchers planted five crops, A, B, C, D and E, in five experimental fields, and only one crop was planted in each experimental field, and one crop was randomly selected from all the arranged crops every year. Q: In three consecutive years, the probability of planting the same crop in experimental field A for at least two years is:

A.36%

48%

52%

D.64%

The first step of analysis is to investigate the probability problem.

Step two, there are many positive solutions. Considering the backward push probability, the backward push of planting the same crop in experimental field A for at least two years is that the crops planted in experimental field A are different every year. Step by step, in the first year of the experimental field, the crop of A can be any kind, and the probability is 1. The crops planted in the second year can't be the same as those planted in the first year, and the probability is that the crops planted in the third year can't be the same as those planted in the previous two years, and the probability is, so the crops planted in the experimental field A are different every year.

Therefore, choose the c option.