# Thread: hypergeometric question

1. ## hypergeometric question

I'm having a little trouble with this question:

A shipment of 20 cameras includes 3 that are defective. What is the minimum number of cameras that must be selected if we require that P(at least 1 defective) $\displaystyle \geq$ 0.8?

any hints would be helpful.

2. Originally Posted by lllll
I'm having a little trouble with this question:

A shipment of 20 cameras includes 3 that are defective. What is the minimum number of cameras that must be selected if we require that P(at least 1 defective) $\displaystyle \geq$ 0.8?

any hints would be helpful.
Assume selection without replacement.

$\displaystyle P(n_{d} \ge 1|N)=1-P(n_{d} = 0|N)$

where we take a saple of size N

So $\displaystyle P(n_d=1|N)\ge 0.8$ is the same as $\displaystyle P(n_d=0|N) < 0.2$

$\displaystyle P(n_d=0|N) =\frac{17}{20}\times \frac{16}{19} \times .. \times \frac{18-N}{21-N}$

Now construct a table of $\displaystyle P(n_d=0|N)$ for $\displaystyle N=1, 2, ..$ and find the smallest
$\displaystyle N$ such that $\displaystyle P(n_d=0|N)<0.2$.

RonL