A carton of 24 bulbs has 6 defective. One bulb is drawn.
(i) Probability it is not defective. (ii) If the first drawn bulb is defective and not replaced, find the probability that a second bulb drawn is defective.
(i) \(\dfrac{3}{4}\); (ii) \(\dfrac{5}{23}\)
Step 1: Understand the total bulbs.
There are 24 bulbs in total. Out of these, 6 are defective and the rest are good.
Step 2: Find the number of good bulbs.
Number of good (non-defective) bulbs = 24 − 6 = 18.
(i) Probability of drawing a bulb that is not defective:
Probability = (Number of good bulbs) ÷ (Total bulbs)
= \(\dfrac{18}{24} = \dfrac{3}{4}\).
(ii) When the first bulb is defective and not replaced:
- If the first bulb is defective, then 1 defective bulb is already taken out.
- So now, defective bulbs left = 6 − 1 = 5.
- Total bulbs left = 24 − 1 = 23.
Step 3: Probability the second bulb is defective:
Probability = (Remaining defective bulbs) ÷ (Remaining total bulbs)
= \(\dfrac{5}{23}\).
Final Answer:
(i) \(\dfrac{3}{4}\)
(ii) \(\dfrac{5}{23}\)