概率论(条件概率)一道题

初级概率论一道条件概率题目，请问(c)怎么做？书上的参考答案只有结果没有过程，谢谢！

sorry i figured out. It was like lottery, no matter when you get the ticket, the first or the last, the prob of wining is K/N, where K is the numebr of winning tickets, and N is total number of tickets.

补充一下，我自己做出来的答案是不带前面(n-m)/(n-1)那一项的，就是只有后面的 m*(k/n)*(n-k)/n, 我感觉答案的更正确，但是不知道怎么推出来的那个(n-m)/(n-1)那一项... 请广大高手告诉我

搜一下variance of hypergeometric distribution

https://mathweb.ucsd.edu/~gptesler/186/slides/186_hypergeom_17-handout.pdf
👆🏻最后两页有

补充内容 (2023-01-13 12:51 +08:00):
重新贴一下网址
mathweb.ucsd.edu/~gptesler/186/slides/186_hypergeom_17-handout.pdf

wzaeng 发表于 2023-1-12 23:49
搜一下variance of hypergeometric distribution

https://mathweb.ucsd.edu/~gptesler/186/slides/186_hyp ...

非常感谢wzaeng  :)

wzaeng 发表于 2023-1-12 23:49
搜一下variance of hypergeometric distribution

https://mathweb.ucsd.edu/~gptesler/186/slides/186_hyp ...

再问一下关于你给的资料。第13页，“The X(i)'s are identically distributed, but dependent. For each ball: P(X(i)=1)=K/N=p..." 请问这里why each ball P(X(i) )=K/N? I know for the first X(i), namely X(1) has the probability of getting green ball of K/N, but for the 2nd ball, it should be (K-1)/(N-1), and for 3rd ball should be (K-2)/(N-2) and so on?  I am not sure why for each ball prob of getting green one is same K/N. Could you clarify a bit? thanks

zyq 发表于 2023-1-14 10:27
再问一下关于你给的资料。第13页，“The X(i)'s are identically distributed, but dependent. For each  ...

因为2nd ball的时候：有2种可能：1）1st green, 2nd green; 2) 1st not green, 2nd green.
1) p = K/N * (k-1)/(n-1); 2) p = (n-k)/n * k/(n-1)
2个概率加在一起就是2nd ball is green = k/n