Question

A shipment of 11 printers contains 2 that are defective. Find the probability that a sample of size 2​, drawn from the 11​, will not contain a defective printer.

Answer 1

The required probability is $\frac{36}{55}$

Solution:

Given, a shipment of 11 printers contains 2 that are defective.  

We have to find the probability that a sample of size 2, drawn from the 11, will not contain a defective printer.

Now, we know that, $\text { probability }=\frac{\text { favourable outcomes }}{\text { total outcomes }}$

Probability for first draw to be non-defective $=\frac{11-2}{11}=\frac{9}{11}$

(total printers = 11; total defective printers = 2)

Probability for second draw to be non defective $=\frac{10-2}{10}=\frac{8}{10}=\frac{4}{5}$

(printers after first slot = 10; total defective printers = 2)

Then, total probability $=\frac{9}{11} \times \frac{4}{5}=\frac{36}{55}$