(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:
Total number of bulbs = 20
Number of defective bulbs = 4
Number of non-defective (good) bulbs = 20 − 4 = 16
(i) Probability of drawing a defective bulb:
Number of favourable outcomes (defective) = 4
Total outcomes = 20
P(defective) = 4/20 = 1/5
(ii) One non-defective bulb is drawn and not replaced.
So now:
- Total bulbs left = 19
- Defective bulbs = 4 (no change)
- Non-defective bulbs = 16 − 1 = 15
Now, we find the probability of drawing a non-defective bulb from the remaining 19 bulbs:
P(non-defective) = 15/19