k****n
发帖数: 98 | 1 急问：
A 药片 和 B 药片形状, 色泽一样.
一批量A 药片出产, 一共20300片. 有四片B 药片混入其中. AB 一共20304片.
A 药片装瓶, 30 片每瓶. 四片B 药片全部装入一瓶的概率是多少?
多谢! |
L*******i
发帖数: 1126 | |
m******i
发帖数: 9479 | 3 (30 choose 4) *(4/20304）^4*(20300)^26
【在 k****n 的大作中提到】
: 急问：
: A 药片 和 B 药片形状, 色泽一样.
: 一批量A 药片出产, 一共20300片. 有四片B 药片混入其中. AB 一共20304片.
: A 药片装瓶, 30 片每瓶. 四片B 药片全部装入一瓶的概率是多少?
: 多谢!
|
D*********Y
发帖数: 3382 | |
a**j
发帖数: 60 | 5 this is a typical hypergeometric distribution. sampling without replacement
answer is very simple
(20300 choose 26)*(4 choose 4)/(20304 choose 30) |
a**j
发帖数: 60 | 6 (20304 choose 30) is the counts for whole sampling space
(20300 choose 26)*(4 choose 4)is the counts for "30 片每瓶. 四片B 药片全部
装入一瓶" |
n**********e
发帖数: 45 | 7 Are you sure it is right?
Simple example: A=4, B=2, 3 tablets/bottle
(4 choose 1)*(2 choose 2) / (6 choose 3) = 4/(5*4)=1/5
the answer should be 2/5
in general, let N=counts/bottle, the result seems to be:
p(B all in a bottle) = ((N-1) choose (B-1))/( (A+B-1) choose (B-1))
【在 a**j 的大作中提到】
: (20304 choose 30) is the counts for whole sampling space
: (20300 choose 26)*(4 choose 4)is the counts for "30 片每瓶. 四片B 药片全部
: 装入一瓶"
|
a****r
发帖数: 1486 | 8 答案就是1/5，你可以做个simulation看看。
【在 n**********e 的大作中提到】
: Are you sure it is right?
: Simple example: A=4, B=2, 3 tablets/bottle
: (4 choose 1)*(2 choose 2) / (6 choose 3) = 4/(5*4)=1/5
: the answer should be 2/5
: in general, let N=counts/bottle, the result seems to be:
: p(B all in a bottle) = ((N-1) choose (B-1))/( (A+B-1) choose (B-1))
|
s*********i
发帖数: 8 | 9 难道这个不是只装一瓶药，4片都装进去的概率吗？实际情况是所有的药都装瓶，4片装
入其中任意一瓶的概率。总瓶数是[20304/30]=677，四片药都装入一瓶的概率是（677
，1）/（677，4）=7.8e－8
replacement
【在 a**j 的大作中提到】
: this is a typical hypergeometric distribution. sampling without replacement
: answer is very simple
: (20300 choose 26)*(4 choose 4)/(20304 choose 30)
|
n**********e
发帖数: 45 | 10 why simulation?
A=4, B=2, N=3
p(B in a bottle)
= p(pick 3 out of A+B, 2 are B) + p(pick 3 out of A+B, none is B)
= (2/6)*(1/5)*3 + (4/6)*(3/5)*(2/4)
=2/5
isn't it?
【在 a****r 的大作中提到】
: 答案就是1/5，你可以做个simulation看看。
|
|
|
a**j
发帖数: 60 | 11 算一下
(20300 choose 26)*(4 choose 4)/(20304 choose 30)
不难吧？
why to simulate?
((20300x...x(20300-26))/26!)/((20304x...x(20304-30))/30!)
=(30x29x28x27)/(20304x20303x20302x20301)
=3.87x10^(-12) |
a****r
发帖数: 1486 | 12 你不觉得你这两个events，是重复的吗？
试试解释一下，“pick 3 out of A+B, 2 are B” 和 “pick 3 out of A+B, none is
B”的区别是什么？
【在 n**********e 的大作中提到】
: why simulation?
: A=4, B=2, N=3
: p(B in a bottle)
: = p(pick 3 out of A+B, 2 are B) + p(pick 3 out of A+B, none is B)
: = (2/6)*(1/5)*3 + (4/6)*(3/5)*(2/4)
: =2/5
: isn't it?
|
c**********e
发帖数: 2007 | 13 Standard solution:
676*30*29*28*27/20304/20303/20302/20301 + 24*23*22*21/20304/20303/20302/
20301.
Or: 676*(30 select 4)/(20304 select 4) + (24 select 4)/(20304 select 4)
Numerically: 2.61841633*20^(-9).
This is the standard answer. |
n**********e
发帖数: 45 | 14 This gives the same answer as I gave before:
(29 choose 3)/(20303 choose 3)
【在 c**********e 的大作中提到】
: Standard solution:
: 676*30*29*28*27/20304/20303/20302/20301 + 24*23*22*21/20304/20303/20302/
: 20301.
: Or: 676*(30 select 4)/(20304 select 4) + (24 select 4)/(20304 select 4)
: Numerically: 2.61841633*20^(-9).
: This is the standard answer.
|
n**********e
发帖数: 45 | 15 ??
These are different events: randomly pick 3 from the A+B pool, you get 2B+1A
in one case and 3A in the other. I don't understand your question
is
【在 a****r 的大作中提到】
: 你不觉得你这两个events，是重复的吗？
: 试试解释一下，“pick 3 out of A+B, 2 are B” 和 “pick 3 out of A+B, none is
: B”的区别是什么？
|
c**********e
发帖数: 2007 | 16 You would be right if the total is divisible by 30, say 20310.
【在 n**********e 的大作中提到】
: This gives the same answer as I gave before:
: (29 choose 3)/(20303 choose 3)
|
c**********e
发帖数: 2007 | 17 This is the probability that all 4 in a specific bottle, say the 1st bottle.
Need to time 677 approximately.
replacement
【在 a**j 的大作中提到】
: this is a typical hypergeometric distribution. sampling without replacement
: answer is very simple
: (20300 choose 26)*(4 choose 4)/(20304 choose 30)
|
a****r
发帖数: 1486 | 18 You are right.
如果假设有m个A，n个B，每个bottle有k个A 和/或 B，一共有p个bottle可以选择，而
要求B都在一个瓶子里，假设n <＝ k
（p choose 1） × （m choose m-k）/ （m+n choose k）
1A
【在 n**********e 的大作中提到】
: ??
: These are different events: randomly pick 3 from the A+B pool, you get 2B+1A
: in one case and 3A in the other. I don't understand your question
:
: is
|
