一次试验中事件A发生的概率为p,独立重复地进行该试验n次这一模型,可以描述许多实际问题,其中的概率公式Pn(A恰好发生k次)=Pn(k)=cnkpk(1-p)n-k,应用非常广泛,下面以概率论中的两道名题为例,谈谈这一模型的确立方法．例1(巴拿赫火柴问题)某数学家随身带着甲、乙两盒火柴,每盒有n根,每次用时,随机地任取一盒,然后从中抽取一根．求:首次发现一盒空时,另一盒恰剩r根火柴的概率(r= 0,1,2,…,n)． The probability of occurrence of event A in a test is p, and the model is repeated repeatedly and repeatedly for this test. It can describe many practical problems. Among them, the probability formula Pn (A happens exactly k times) = Pn(k) = cnkpk (1 -p) nk, the application is very extensive, the following two questions in probability theory as an example, talk about the establishment of this model. Example 1 (Banatch Match Question) A mathematician carries two boxes of match A and B. Each box has n roots. Each time they are used, they randomly take a box and then take one from them. Seeking: When the first time a box is found empty, the probability that another box has r matches (r = 0, 1, 2, ..., n) remains.