Question

A pack contains $4$ blue, $2$ red and $3$ black pens. If $2$ pens are drawn at random from the pack, NOT replaced and then another pen is drawn. What is the probability of drawing $2$ blue pens and $1$ black pen?

• A. $\frac{6}{14}$
• B. $\frac{3}{14}$
• C. $\frac{1}{14}$
• D. none of these

Answer 1

The correct option is C $\frac{1}{14}$

Total number of pens $=9$

Probability of drawing 1 blue pen = $\frac{4}{9}$

Probability of drawing another blue pen = $\frac{3}{8}$

Probability of drawing 1 black pen = $\frac{3}{7}$

Probability of drawing 2 blue pens and 1 black

pen = $\frac{4}{9}\times \frac{3}{8}\times \frac{3}{7}=\frac{1}{14}$