g*******d 发帖数: 16 | 1 房间里有四个人,对于任何两个人,他们是朋友的概率是50%。
两个人只要满足下面三个条件之一就可以称作是有关系的,
1。他们是朋友。
2。他们有共同的朋友。
3。他们各自的朋友,彼此之间是朋友。譬如,甲有朋友丙,乙有朋友丁,丙和丁是朋
友。
现在要问,房间里每一对都有关系的概率是多少? | g*******d 发帖数: 16 | | l*****e 发帖数: 65 | 3
Is this a graph problem? Four points, an edge stands for the friendship,
then two points have relationship when they are connected by a path.
If there are at least four edges, then the graph is connected. If there are
three edges, only four cases are not connected. The graphs are isomorphic
though, namely a triangle with an isolated point.
Thus the answer of your question is
[C(6,4) + C(6,5) +C(6,6) + C(6,3)-4] /2^6 = 19/32.
Does this agree with your answer?
【在 g*******d 的大作中提到】 : 房间里有四个人,对于任何两个人,他们是朋友的概率是50%。 : 两个人只要满足下面三个条件之一就可以称作是有关系的, : 1。他们是朋友。 : 2。他们有共同的朋友。 : 3。他们各自的朋友,彼此之间是朋友。譬如,甲有朋友丙,乙有朋友丁,丙和丁是朋 : 友。 : 现在要问,房间里每一对都有关系的概率是多少?
| g*******d 发帖数: 16 | 4
are
Yes, sir. It's a graph problem and your answer is right.
【在 l*****e 的大作中提到】 : : Is this a graph problem? Four points, an edge stands for the friendship, : then two points have relationship when they are connected by a path. : If there are at least four edges, then the graph is connected. If there are : three edges, only four cases are not connected. The graphs are isomorphic : though, namely a triangle with an isolated point. : Thus the answer of your question is : [C(6,4) + C(6,5) +C(6,6) + C(6,3)-4] /2^6 = 19/32. : Does this agree with your answer?
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