机率题

無聊人

three balls are thrown at random into five bowls so that each ball has the same chance of going into any bowl independently of wherever the other 2 balls fall. determine the prob distribution of the number of empty bowls

是不是要酱写
Let R be the number of empty bowls

P(R=2) = ...
P(R=3) = ...

以此类推？
如果是的话，怎么做呢？

puangenlun

p(r=1)=0
p(r=2)=5C3
p(r=3)=3C2*5C1*4C1
p(r=4)=3C3*5C1
p(r=5)=0

大致如此，也许有误，还望多多指教。

flash

p(r=1)=0
p(r=2)=5C3
p(r=3)=3C2*5C1*4C1
p(r=4)=3C3*5C1
p(r=5)=0

大致如此，也许有误，还望多多指 ...
puangenlun 发表于 24-1-2010 11:35 AM

题目既然是要求 probability distribution，那么答案应该是求各种情况的机率。个人认为应该是   

p(r=0)=0
p(r=1)=0
p(r=2)=5C1*4C1*3C1/125
p(r=3)=3C2*5C1*4C1/125
p(r=4)=5C1/125
p(r=5)=0

無聊人

原来是这样，谢谢！