(i) 4 defective pens are accidentally mixed with 16 good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is drawn at random from the lot. What is the probability that the pen is defective ?

(ii) Suppose the pen drawn in (i) is defective and is not replaced. Now one more pen is drawn at random from the rest. What is the probability that this pen is :

(a) defective ?

(b) not defective ?

(i) No. of pens = 20 (4 + 16)

∴ No. of possible outcomes = 20.

Since, there are 4 defective pens,

∴ No. of favourable outcomes = 4.

P(drawing a defective pen) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{4}{20} = \dfrac{1}{5}$.

Hence, probability of drawing a defective pen = $\dfrac{1}{5}$.

(ii) Since, pen drawn is defective.

So, no. of pens left = 19 and no. of defective pens left = 3.

(a) No. of favourable outcomes (drawing a defective pen) = 3.

No. of possible outcomes = 19

P(drawing a defective pen) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{3}{19}$.

Hence, probability of drawing a defective pen = $\dfrac{3}{19}$.

(b) No. of favourable outcomes (drawing a good pen) = 16.

No. of possible outcomes = 19

P(drawing a good pen) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{16}{19}$.

Hence, probability of drawing a not defective pen = $\dfrac{16}{19}$.