Argh..it is so annoying. I'm looking at the first answer and now it seems so obvious. But yet I can't see why the answer is 0,40591 for the second one :(
Ah..I think I see it. If we know the probability that all five are perfect, given n=10, then we know that the last five must contain the defective one. And with 1-0,59049 we find just what that probability is, right?
no, even when you set n to 10 you don't know how many of them are damaged, it could even be all of them.
So, seting a value for n doesn't help you.
Good thing is that the solution is even simpler :)
For picking 5 chips you know that only six things can occur: 0, 1, 2, 3, 4 or 5 chips are defective. Thus giving you a combined probablity of 1.
Now, for the second answer you are looking for the probability of either 1,2,3,4 or 5 defective chips, and you already have the probablity for 0 defective chips.
So, you calculate: (probability of 1 or more defective chips) = 1 - (probability of 0 defective chips)
But I'm still not convinced that what I wrote was wrong ;) Because if you set n=10, and you know it's only 10% that has a defect, then there can only be 1/10 with that defect (obviously). So if the first five a perfect, then the defect one can't be anywhere else but in the last five, because the last five can't have anything else than [perfect, perfect, defect, perfect, perfect]. Of course in a random order ;)
Edited by Kirsebaer at 21:13 UTC, 10 September 2010
what you wrote just doesn't work as an explanation, as you are trying to explain a more general case with a specific example based on an assumption.
also, the probability of having exactly one defective chip in a group of 10 chips is just 38,7%, and having exactly one defective chips in a batch of 5 is 32,8%
Anyway, what you should use to calculate such things is this:
But what does it all mean p0rt?!?! Why is the error produced by the linear approximation of the probabilty that was calculated using a constant population equal to the difference between said probability and the one calculated when using a decreasing population? Perhaps you could enlighten us?