A lot of 20 bulbs contain 4 defective ones.
Question:

(i) A lot of 20 bulbs contain 4 defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective?

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

Solution:

(i) Total number of bulbs = 20

Total number of defective bulbs = 4

$P($ getting a defective bulb $)=\frac{\text { Number of favourable outcomes }}{\text { Numher of total nossible outcomes }}$

$=\frac{4}{20}=\frac{1}{5}$

(ii) Remaining total number of bulbs = 19

Remaining total number of non-defective bulbs = 16 − 1 = 15

$P($ getting a not defective bulb $)=\frac{15}{19}$