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同学们来帮忙解个题吧~

同学们来帮忙解个题吧~# JobHunting - 待字闺中

m*12012-05-23 07:05

1 楼

You have a chest of 8 drawers. With probability 1/2, you put a letter in one
of the drawers. With probability 1/2, you don't put a letter in any drawer.
I open the first 7 drawers, all are empty. What is the probability there is
a letter in the 8th drawer?

b*72012-05-23 07:05

2 楼

我也觉得是1/9。
可以转化成一个物品放入16个抽屉之一。开了7个没看到。开第八个看到的可能性是1/9。

O*22012-05-23 07:05

3 楼

1／2
因为每开一个空的抽屉，都增大了在最后一个抽屉里的可能

【在 b*****7 的大作中提到】

: 我也觉得是1/9。
: 可以转化成一个物品放入16个抽屉之一。开了7个没看到。开第八个看到的可能性是1/9。

j*e2012-05-23 07:05

4 楼

这是个后验条件概率问题。
A表示信放进任一个抽屉，D=i表示信放进了第i给抽屉。
P(A) = 0.5, P(D=i|A)=1/8, P(D=i)=1/16
现在要求的是P(D=8|D!=1,2,...,7).
P(D=8|D!=1,2,...7) * P(D!=1,2,...,7) = P(D=8) = 1/16.
P(D!=1,2,...,7) = P(!A) + P(A and D=8) = 1/2 + 1/16 = 9/16
所以P(D=8|D!=1,2,...,7) = 1/9.

one
drawer.
is

【在 m*******1 的大作中提到】

: You have a chest of 8 drawers. With probability 1/2, you put a letter in one
: of the drawers. With probability 1/2, you don't put a letter in any drawer.
: I open the first 7 drawers, all are empty. What is the probability there is
: a letter in the 8th drawer?

j*e2012-05-23 07:05

5 楼

这个转化很有意思

/9。

【在 b*****7 的大作中提到】

: 我也觉得是1/9。
: 可以转化成一个物品放入16个抽屉之一。开了7个没看到。开第八个看到的可能性是1/9。

x*y2012-05-23 07:05

6 楼

I remember a similar but famous 3-gate problem:
there are 3 gates, behind one and only one of which there is a gift. You
select one gate, and of the other 2 gates, one that does not have gift is
removed. Now, there are only 2 gates left, you can switch. Should you do it?
The answer is yes, as the other door has the probablity of 2/3 to have the
gift. The conditional probability does not apply here is because they are not really independent any more; after the removal, the remaining two gates are not
really equal.