Question

A shipment of 12 printers contain 3 that are defective . Find the probability that a sample 5 drawn from the twelve will have a defective printer

Answer 1

There are total 12 printers in which 3 are defective.

And there is a sample of 5 drawn from the 12 printers,

Then the total number of ways you can get 5 printers is

$12_{C_5}$

The total number of ways you can get 5 working printers is

$9_{C_5}$

The probability of (no defectives) is

$\frac{9_{C_{5_{}}}}{12_{C_5}}$

We have to determine the probability that a sample 5 drawn from the twelve will have a defective printer

$1-P(nodefective)=1-\frac{9_{C_5}}{12_{C_5}}$$1-\frac{126}{792}=\frac{792-126}{792}$$\frac{666}{792}=0.84$

Hence the probability that a sample 5 drawn from the twelve will have a defective printer is

$0.84$