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题目袋中放有大小相同的m个黑球和n个白球.现逐个从袋中取球,若每次取出球后再放回,显然每次取得黑球的概率均为mm+n;若每次取出的球不再放回,则第k次取得黑球的概率是多少(1≤k≤m+n)?思路1这是一个典型的古典概型问题:前k次逐个取球,相当于从m+n个球中任取k个球作一排列,样本空间中的基本事件共有Akm+n个,而事件“第k次取得黑球”表明第k个球为黑球,共包含C1mAk-1m+n-1个基本事件,故第k次取得黑球的概率为
The title bag contains m black balls of the same size and n white balls, and one by one, the ball is taken one by one from the bag. If the ball is removed after each removal, the probability of obtaining the black ball each time is mm + n. Each time the ball is no longer put back, the probability of getting the black ball k times (1 ≤ k ≤ m + n)? This is a classic classical problem: the first k times one by one to take the ball, Equivalent to taking k balls from m + n balls as an arrangement, the basic events in the sample space have Akm + n in total, and the event “getting the black ball k times” indicates that the kth ball is a black ball , Contains a total of C1mAk-1m + n-1 basic events, so the probability of getting the black ball k times