Question

A shipment of nine printers contains two they are defective. Find the probability that a sample of size 2, drawn from nine, will not contain a defective printer

Answer 1

The shipment contains 9 printers and 2 are defective. 2 printers are chosen at random.

2 out of 9 can be chosen in $n=C_9^2$ ways (Total number of outcomes)

Number of favourable outcomes (not containing defective)

$m=C_{9-2}^2=C_7^2$

The Probability that none is defective is

$p =\dfrac{m}{n}=\dfrac{C_7^2}{C_9^2}=\dfrac{7}{12}$

$=\dfrac{7}{12}$