h*******o
发帖数: 169 | 1 there are N balls. Out of the N balls, there are M black balls and N-M while
balls. Permutate all balls in a round circle. What is the probability that
at least X black balls are in a row (e.g., WWBBBBBWWWWBWBW....)? Please note
the balls are permutated in a round circle.
Thanks in advance for any help!!!!!!!!! | h*******o
发帖数: 169 | 2 Please, no one can help? Is it often seen in probability class? I really
need some help here:(
while
that
note
【在 h*******o 的大作中提到】
: there are N balls. Out of the N balls, there are M black balls and N-M while
: balls. Permutate all balls in a round circle. What is the probability that
: at least X black balls are in a row (e.g., WWBBBBBWWWWBWBW....)? Please note
: the balls are permutated in a round circle.
: Thanks in advance for any help!!!!!!!!!
| w******o
发帖数: 726 | 3 Let K=N!/M!/(N-M)!;! means 阶乘.
P(X>=x)=\sum_{i=x}^M (N-i)!/(M-i)!/(N-M)!/K;
while
that
note
【在 h*******o 的大作中提到】
: there are N balls. Out of the N balls, there are M black balls and N-M while
: balls. Permutate all balls in a round circle. What is the probability that
: at least X black balls are in a row (e.g., WWBBBBBWWWWBWBW....)? Please note
: the balls are permutated in a round circle.
: Thanks in advance for any help!!!!!!!!!
| h*******o
发帖数: 169 | 4 Thanks for replying!! Could you please give some explanation for this answer?
1) It seems to me that K should be the No. of all possible permutations.
However, isn't that N! then? What is your K calculating?
2) The numerator seems to be the sum of the number of permuations that has x
black balls in a row, x+1 black balls in a row, ..., until M black balls in
a row. But I don't know how you get this.
Could you please give the orignal expression without simplification? I
really need to understand
【在 w******o 的大作中提到】
: Let K=N!/M!/(N-M)!;! means 阶乘.
: P(X>=x)=\sum_{i=x}^M (N-i)!/(M-i)!/(N-M)!/K;
:
: while
: that
: note
| h*******o
发帖数: 169 | 5 Hello, anyone here can help? Thanks!
answer?
x
in
【在 h*******o 的大作中提到】
: Thanks for replying!! Could you please give some explanation for this answer?
: 1) It seems to me that K should be the No. of all possible permutations.
: However, isn't that N! then? What is your K calculating?
: 2) The numerator seems to be the sum of the number of permuations that has x
: black balls in a row, x+1 black balls in a row, ..., until M black balls in
: a row. But I don't know how you get this.
: Could you please give the orignal expression without simplification? I
: really need to understand
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