Question

Consider another example where a pack contains 4 blue, 2 red and 3 black pens. If 2 pens are drawn at random from the pack, replaced and then another pen is drawn. What is the probability of drawing 2 blue pens and 1 black pen?

• A. $\frac{1}{81}$
• B. $\frac{2}{81}$
• C. $\frac{1}{3}$
• D. $\frac{1}{9}$

Answer 1

The correct option is B $\frac{2}{81}$

Total number of pens = 9The probability of drawing 2 blue pens out of 9 pens $=\frac{2}{9}$.

After the first draw, the pens are replaced, which means the number of pens in the pack is still 9.

Hence, the probability of drawing 1 black pen from the pack $=\frac{1}{9}$So the total probability of drawing 2 blue and 1 black pen would be $\frac{2}{9}\times \frac{1}{9}=\frac{2}{81}$.