hypergeometric question

**lllll** · March 15th 2008, 10:08 PM

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) $\geq$ 0.8?

any hints would be helpful.

**CaptainBlack** · March 15th 2008, 11:43 PM

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) $\geq$ 0.8?

any hints would be helpful.

Assume selection without replacement.

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

where we take a saple of size N

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

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

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

RonL

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