e-Statistics > 4470-5470 Probability and Statistics I

Hypergeometric distribution

A lot of $ n$ items contains $ k$ defectives, and $ m$ are selected randomly and inspected. How should the value of $ m$ be chosen so that the probability that at least one defective item turns up is 0.9? Apply your answer to the following cases:
  1. $ n=1000$ and $ k=10$;
  2. $ n=10,000$ and $ k = 100$.

Suppose that we have a lot of size $ n$ containing $ k$ defectives. If we sample and inspect $ m$ random items, what is the probability that we will find $ i$ defectives in our sample? This probability is called a hypergeometric distribution, and expressed by

$\displaystyle p(i) = \frac{\displaystyle{k \choose i} {n-k \choose m-i}}
{\displaystyle{n \choose m}},
\quad i = \max\{0,m+k-n\},\ldots,\min\{m,k\}
$

Given $ n=$ and $ k=$ in the hypergeometric distribution, the smallest value $ m=$ can be determined so that $ 1 - p(0) \ge$ .