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?
|
|
