求助难题

清月依云

已解决。谢谢。

sdcar2010

2N/3: 0,1,2,3 不合格
N/5: 0,1 不合格
2N/15:0,1 不合格

全部n个产品里，刚好有2个不合格: 0+1+1; 1+1+0; 1+0+1; 2+0+0; total 4 possibilities
Total possibilities = 4*2*2=16 possibilities
Probability = 4/16 =1/4

清月依云

2N/3: 0,1,2,3 不合格
N/5: 0,1 不合格
2N/15:0,1 不合格

全部n个产品里，刚好有2个不合格: 0+1+1; 1+1+0; 1+0+1; 2+0+0; total 4 possibilities
Total possibilities = 4*2*2=16 possibilities
Probability = 4/16 =1/4

-- by 会员 sdcar2010 (2011/4/9 20:59:33)

非常谢谢你，不过题目是2n/3, 2n/5,n/5啊~我照你这个方法算是5/24，但是感觉不对，因为总的是n，2n/3+2n/5+n/5不等于n啊～还有神马算法吗？

sdcar2010

The key is to figure out how to calculate the maximal number of bad products in (2N/15) products.

We know that every N/5 products have no more than 1 bad product. And we know that 2N/5, no more than 2. And 2N/3 , no more than 3. And 4N/5, no more than 4.

Therefore, (4N/5 - 2N/3) = 2N/15 will not have more than (4-3) = 1 bad product.

That's why I put 0, 1 for (2N/15) products!

2/3 + 1/5 + 2/15 = 1

brisk827

那可以請說明一下為何不是採納題目所給的 2N/5: 0,1,2 不合格?
若此用2N/15，題目所給2N/5的用意是?

感謝!

barbiebear

话说我看晕了~~~

但是继续请教SDcar，怎么我的思路里觉得这个逻辑有点点问题啊？
首先，你用的是We know that every N/5 products have no more than 1 bad product. And we know that 2N/5, no more than 2.
这里“每N/5 products have no....”和 “N/5 products have no ....."意思不一样啊，这样就等于换了概念
如果这里题目是表达每 N/5, 那么就不用告诉我们 2N/5 products have no more than 2了吧。

即使这里是  every N/5....., 那么你的解法里应该是用题目条件推出  4N/5, no more than 4. 如果可以这样推的话，那是不可以直接推N个里面have no more than 5呢？
这样子，按照你的解法思路，那就是
N:0,1,2, 3, 4, 5
有两个的就是 N里刚好有2， 一种possibility
那么一共有6种 possibilities
所以， 1/6

我知道这个思路完全错啦~~~ 但是我就这么想下来了，一坨浆糊！
大家指正

清月依云

我还是没看懂...555～～原谅我的智商问题...

fengchen318

同问~

sdcar2010

话说我看晕了~~~

但是继续请教SDcar，怎么我的思路里觉得这个逻辑有点点问题啊？
首先，你用的是We know that every N/5 products have no more than 1 bad product. And we know that 2N/5, no more than 2.
这里“每N/5 products have no....”和 “N/5 products have no ....."意思不一样啊，这样就等于换了概念
如果这里题目是表达每 N/5, 那么就不用告诉我们 2N/5 products have no more than 2了吧。

即使这里是  every N/5....., 那么你的解法里应该是用题目条件推出  4N/5, no more than 4. 如果可以这样推的话，那是不可以直接推N个里面have no more than 5呢？
这样子，按照你的解法思路，那就是
N:0,1,2, 3, 4, 5
有两个的就是 N里刚好有2， 一种possibility
那么一共有6种 possibilities
所以， 1/6

我知道这个思路完全错啦~~~ 但是我就这么想下来了，一坨浆糊！
大家指正

-- by 会员 barbiebear (2011/4/9 22:37:56)

Good argument. For this question, I prefer to have A has not more than 3, B has no more than 2, c has no more than 1, and A+B+C =N.  Then the things would become quite easy. Unfortunately 2/3 + 2/5 >1. So we cannot simply plug in those numbers.

Then the question is how to get the N exactly!

Basically 2N/5 and N/5 talk about the same thing. You just treat these two conditions as the same.

Then you have to plug in the 2N/3 condition. Now we are limited to ONLY 2N/3 and N/5. The difference between them and N is 2N/15. We need to know what is the POSSIBLE maximum number of products that are bad in 2N/15 products! One (1) is the answer as I just deduced above. It cannot be more than 1.

As to why not use ONLY 2N/5 and N/5 conditions, the reason is that you are omitting the 2N/3 condition by limiting yourself to 2N/5 and N/5!

sdcar2010

So the take home message is the following:

Figure out how to have A has no more than a bad products, B has no more than b bad products, C has no more than c bad products, and A+B+C =N. Most likely you will have to calculate the last condition from the combination of the first two.

It's rather simple if you follow this route.