The application scope of Bernoulli's probability formula PN (k) = CN ^ k * P ^ k * (1-p) ^ (n-k)

In the case of binary distribution, such as the coin toss problem, the following conditions apply
1. All events are independent
2. There are only two results for each event, one is p, the other is 1-p

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1. If the probability of having n children in a family is: PN = α p ^ n, let the birth rates of boys and girls be equal, find the probability of having K boys in the family? In addition, if there is at least one boy in the family, find the probability of having at least 2 boys in the family; if there is no girl in the family, find the probability of having exactly one boy
2. Suppose that the probability of success of one test is p, and 100 independent repeated tests are carried out=______ The standard deviation of success times is the largest, and the maximum value is______ ．
3. The average value of a group of data is 153.2, and the standard deviation is 9.36. The probability that the value is greater than or equal to 160 When any data in the group is selected is calculated
4. When the sample size is 100 cases, the probability of X average value less than or equal to 700 g is calculated
5. Given that the average is 100 and the standard deviation is 20, the probability of greater than or equal to 120 and less than or equal to 55 can be selected
6. Mathematical standard deviation What is the standard deviation of 1,2,3,4,5?
7. The probability of a appearing at least once in four independent repeated events is 0.59. What is the probability of a appearing in one test?
8. If the probability of event a occurring at least once in four independent repeated tests is 8081, then the probability of event a occurring in one test is 8081______ ．
9. (2014 · anqing simulation) in three independent repeated tests, the probability of event a occurring in each test is the same. If the probability of event a occurring at least once is 6364, the probability of event a occurring just once is () A. 14B. 34C. 964D. 2764
10. Senior high school mathematics problems (independent repeated test) 1. Assuming that the probability of event a occurring at least once in four independent repeated experiments is 80 / 81, try to find the probability of event a occurring in another experiment 2. Someone shoots at a target until it is hit. The probability of each shot hitting the target is 1 / 3. Calculate the probability of hitting the target for the nth time
11. In one experiment, the probability of event a occurrence is p. in n independent repeated experiments, the probability of event a occurrence for odd number of times is calculated. [1 - (1-2p) ^ 2] / 2
12. For the event with probability p, the probability of event occurrence > = k times in n independent repeated tests Probability p event, the probability of K times of event occurrence in n independent repeated tests P (x = k) = C (n, K) * P ^ k * (1-p) ^ (n-k), what function is convenient to calculate: the probability of event occurrence > = k times in n independent repeated tests
13. It is known that the probability of event a in a test is p (0
14. Let the probability of event a be p = P (a). Now repeat the experiment n times independently, and try to find the probability of a appearing at least once
15. If an experiment has N equal possible results, and event a occurs when one of M results occurs, then the probability of event a occurrence P (a)=
16. Calculation of inflation rate Consider the impact of inflation in a two person economy: Bob is a soybean farmer and Rita is a rice farmer. They always consume the same amount of rice and soybeans. In 2008, soybeans cost $1 and rice $3 Suppose the price of soybeans is $2 and the price of rice is $4 in 2009. What is the inflation rate? Suppose the price of soybean is $2 and the price of rice is $1.50 in 2009. What is the inflation rate?
17. How to calculate the inflation rate Assuming that the annual CPI is 3%, how much is the 8W after 35 years compared with the present?
18. Write the chemical symbol expression of the following changes: (1) A dark red powder burns in oxygen and produces a lot of white smoke (2) A pale yellow powder burns in the air, giving off a faint pale blue flame (3) A silvery white metal burns in oxygen to give off a dazzling white light (4) A kind of black powder burns violently in oxygen and emits white light
19. Write the chemical symbol expressions for the following reactions: Charcoal burns in oxygen—— Red phosphorus burns in air—— Sulfur burns in air—— 4 heating potassium permanganate to produce oxygen—— Heating mixture of potassium chlorate and manganese dioxide——
20. Write the following expressions and symbols Preparation of oxygen by heating potassium permanganate Preparation of oxygen from hydrogen peroxide and manganese dioxide Preparation of oxygen by heating potassium chlorate and manganese dioxide Red phosphorus burns in the air The wire burns in oxygen Charcoal burns in the air