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(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 not replaced. Now bulb is drawn at random from the rest. What is the probability that this bulb is not defective?
Given:
A lot of 20 bulbs contain 4 defective ones. One bulb is drawn at random from the lot.
To do:
We have to find the probability that (i) this bulb is defective.
(ii) If the bulb drawn in (i) is not defective and not replaced and now the bulb is drawn at random from the rest. We have to find the probability that this bulb is not defective.
Solution:
(i) Total number of bulbs $n=20$
Number of defective bulbs $=4$
This implies,
The number of non defective bulbs $=20-4=16$
The probability that the bulb is defective $=\frac{4}{20}$
$=\frac{1}{5}$
(ii) One bulb taken out is not replaced and is not a defective one.
This implies,
Number of remaining bulbs $=20-1=19$
Number of bulbs that are not defective $=16-1=15$
The probability that the bulb is not defective $=\frac{15}{19}$.
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