s********t
发帖数: 31 | 1 In Crack book:
Problem 1:
I tell you that I have two kids and that one of them is a girl (I say
nothing about the other). What is the probablility of that I have two girls?
Answer: 1/3
Problem 2:
I tell you that I have two kids and that one of them is a girl (I say
nothing about the other). And you seen I am walking with one of my kid and
the kid is a girl. What is the probablility of that I have two girls?
Answer: 1/2
I am kind of dumb and still not figured out the subtle difference between | s****n
发帖数: 1237 | 2 You can think of the event space, under classical probability theory, the
two kids are distinguishable. The total space = (BB,BG,GB,GG)
P1: You know there's a G, so the subspace is (BG,GB,GG), P(GG) under this
conditional space = 1/3
P2: You see one kid is girl, if this is the first kid, subspace is (GB,GG),
P(GG)=1/2; if it's the 2nd kid, subspace is (BG,GG), P(GG)=1/2. So it's
always 1/2
girls?
and
【在 s********t 的大作中提到】
: In Crack book:
: Problem 1:
: I tell you that I have two kids and that one of them is a girl (I say
: nothing about the other). What is the probablility of that I have two girls?
: Answer: 1/3
: Problem 2:
: I tell you that I have two kids and that one of them is a girl (I say
: nothing about the other). And you seen I am walking with one of my kid and
: the kid is a girl. What is the probablility of that I have two girls?
: Answer: 1/2
| s********t
发帖数: 31 | 3 Thanks much.
But in problem 1, what is wrong to just look at the event space of the other kid. It will be a B or G with equal possibility. This leads to answer of 1/2. What is wrong here? | t***s
发帖数: 4666 | 4 because you don't know the "one girl" is the first kid or second.
other kid. It will be a B or G with equal possibility. This leads to
answer of 1/2. What is wrong here?
【在 s********t 的大作中提到】
: Thanks much.
: But in problem 1, what is wrong to just look at the event space of the other kid. It will be a B or G with equal possibility. This leads to answer of 1/2. What is wrong here?
| s********t
发帖数: 31 | 5 In problem 1, does the "one girl told" being 1st or 2nd kid really matter?
What is wrong if I only need to consider the other kid.
Still do not know the fundamental difference between the two problems?
Strongly looking for something persuisive and clear (for me - I am dumb).
【在 t***s 的大作中提到】
: because you don't know the "one girl" is the first kid or second.
:
: other kid. It will be a B or G with equal possibility. This leads to
: answer of 1/2. What is wrong here?
| t***s
发帖数: 4666 | 6 when you see a kid, the kid is fixed. when you are told there is
a girl, you don't know whether it's the first kid or second, so
it is not fixed
【在 s********t 的大作中提到】
: In problem 1, does the "one girl told" being 1st or 2nd kid really matter?
: What is wrong if I only need to consider the other kid.
: Still do not know the fundamental difference between the two problems?
: Strongly looking for something persuisive and clear (for me - I am dumb).
| s********t
发帖数: 31 | 7 TDS,
This makes a lot of sense. You are good and warmhearted...
This problme makes me sleepless and foodless. Thanks.
【在 t***s 的大作中提到】
: when you see a kid, the kid is fixed. when you are told there is
: a girl, you don't know whether it's the first kid or second, so
: it is not fixed
:
:
| p*****k
发帖数: 318 | 8 solarquant, this type of questions are usually dubious, strongly
depending on the interpretation and assumptions.
there was a nice discussion here:
http://www.wilmott.com/messageview.cfm?catid=26&threadid=77882 | c*********g
发帖数: 154 | 9 这个是典型的Bayesian Inference啊。在用Bayesian的时候，最重要的是分清什么是先
验和后验，其实说到底，就是分清楚原因（或者叫状态）和结果（或者叫观测）。所以
一般的做法都是这样的：
1.列出所有可能的原因（状态）及其先验。对于这两道题，状态集合是{BB,BG,GB,GG}
，并且P(BB)=P(BG)=P(GB)=P(GG)=1/4,
2.列出从各原因（状态）到结果（观测）的条件概率分布（离散的或连续的）。
对于Problem 1: P(告诉别人我有一个女孩 | BB) = 0,
P(告诉别人我有一个女孩 | BG) = 1,
P(告诉别人我有一个女孩 | GB) = 1,
P(告诉别人我有一个女孩 | GG) = 1,
对于Problem 2：P(别人看到我有一个女孩 | BB) = 0,
P(别人看到我有一个女孩 | BG) = 1/2,
【在 s********t 的大作中提到】
: In Crack book:
: Problem 1:
: I tell you that I have two kids and that one of them is a girl (I say
: nothing about the other). What is the probablility of that I have two girls?
: Answer: 1/3
: Problem 2:
: I tell you that I have two kids and that one of them is a girl (I say
: nothing about the other). And you seen I am walking with one of my kid and
: the kid is a girl. What is the probablility of that I have two girls?
: Answer: 1/2
| t***s
发帖数: 4666 | 10 of course the big assumption for prob 2 is that i'm not trying to
distort the distribution by only walking with my daughter. if
that's the case, the prob 2 becomes prob 1.
【在 c*********g 的大作中提到】
: 这个是典型的Bayesian Inference啊。在用Bayesian的时候，最重要的是分清什么是先
: 验和后验，其实说到底，就是分清楚原因（或者叫状态）和结果（或者叫观测）。所以
: 一般的做法都是这样的：
: 1.列出所有可能的原因（状态）及其先验。对于这两道题，状态集合是{BB,BG,GB,GG}
: ，并且P(BB)=P(BG)=P(GB)=P(GG)=1/4,
: 2.列出从各原因（状态）到结果（观测）的条件概率分布（离散的或连续的）。
: 对于Problem 1: P(告诉别人我有一个女孩 | BB) = 0,
: P(告诉别人我有一个女孩 | BG) = 1,
: P(告诉别人我有一个女孩 | GB) = 1,
: P(告诉别人我有一个女孩 | GG) = 1,
|
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