Question

In a box of $12$ pens, a total of $3$ are defective. If a customer buys $2$ pens selected at random from the box, what is the probability that neither pen will be defective?

• A. $\frac{1}{6}$
• B. $\frac{2}{9}$
• C. $\frac{6}{11}$
• D. $\frac{9}{16}$
• E. $\frac{3}{4}$

Answer 1

The correct option is C $\frac{6}{11}$

Probability of the 1st pen being good = # of favorable outcomes / # of total outcomes $=\frac{9}{12}.$

Probability of the 2nd pen being good = # of remaining favorable outcomes / # of total remaining outcomes $=\frac{8}{11}$

Total probability $=\frac{9}{12}\ast \frac{8}{11}=\frac{6}{11}$